Hello students!!! Are you searching for the Grade 4 Answer Key of Go Math Chapter 13 Algebra: Perimeter and Area. Then what are you waiting for Download Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area pdf for free of cost here. Make our Go Math Grade 4 Chapter 13 Solution Key as a reference while practicing for your exams. Check out the topics covered in Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area from the below.

## Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area

Students can get the solution for only for the exercises and homework problems but also for the Mid-Chapter checkpoint and review test. So, the students who are practicing seriously for the exams can go through the Go Math 4th Grade Key of Chapter 13 Perimeter and Area. You can test your knowledge by solving the problems in this HMH Go Math Grade 4 Answer Key Chapter Perimeter and Area.

### Common Core – New – Page No. 721

**Perimeter**

**Find the perimeter of the rectangle or square.**

Question 1.

9+3+9+3=24

24 inches

Explanation:

Length = 9 inches

Width = 3 inches

Perimeter of the rectangle = l + w + l + w

9+3+9+3=24

Therefore the Perimeter of the rectangle = 24 inches.

Question 2.

_____ meters

Answer: 32 meters

Explanation:

Side of a square = 8 meters

The perimeter of a square = 4a

= 4 × 8 meters = 32 meters

Thus the perimeter of a square = 32 meters.

Question 3.

_____ feet

Answer: 44 feet

Explanation:

Length = 10 ft

Width = 12 ft

Perimeter of the rectangle = l + w + l + w

P = 10 + 12 + 10 + 12 = 20 + 24 = 44 feets

Thus the perimeter of the rectangle = 44 feet.

**Remember: perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a rectangle, opposite sides are equal in length, so the perimeter is twice its width plus twice its height.**

Question 4.

_____ centimeters

Answer: 108 centimeters

Explanation:

Length = 30 cm

Width = 24 cm

Perimeter of the rectangle = l + w + l + w

= 30 + 24 + 30 + 24 = 60 + 48

= 108 centimeters

Therefore the perimeter of the rectangle = 108 centimeters

Question 5.

_____ inches

Answer: 216 inches

Explanation:

Length = 25 in.

Width = 83 in.

Perimeter of the rectangle = l + w + l + w

= 25 + 83 + 25 + 83

= 216 inches

Thus the perimeter of the rectangle = 216 inches

Question 6.

_____ meters

Answer: 240 meters

Explanation:

The side of a square = 60 meters

The perimeter of the square = 4a

= 4 × 60 meters = 240 meters

Thus the perimeter of the square = 240 meters.

**Problem Solving**

Question 7.

Troy is making a flag shaped like a square. Each side measures 12 inches. He wants to add ribbon along the edges. He has 36 inches of ribbon. Does he have enough ribbon? Explain.

_____

Answer: No. He needs 48 inches of ribbon.

Explanation:

Troy is making a flag shaped like a square. Each side measures 12 inches.

He wants to add a ribbon along the edges.

He has 36 inches of ribbon.

36 inches + 12 inches = 48 inches

Question 8.

The width of the Ochoa Community Pool is 20 feet. The length is twice as long as its width. What is the perimeter of the pool?

_____ feet

Answer: 120 feet

Explanation:

The width of the Ochoa Community Pool is 20 feet.

The length is twice as long as its width.

Length = 2 × 20 feet = 40 feet

Perimeter of the rectangle = l + w + l + w

= 40 + 20 + 40 + 20 = 120 feet

Thus the perimeter of the pool is 120 feet.

### Common Core – New – Page No. 722

**Lesson Check**

Question 1.

What is the perimeter of a square window with sides 36 inches long?

Options:

a. 40 inches

b. 72 inches

c. 144 inches

d. 1,296 inches

Answer: 144 inches

Explanation:

Given, Side of a square = 36 inches

The perimeter of the square = 4 × side = 4a

= 4 × 36 inches = 144 inches

Thus the perimeter of the square = 144 inches

The correct answer is option C.

Question 2.

What is the perimeter of the rectangle below?

Options:

a. 11 meters

b. 14 meters

c. 18 meters

d. 400 meters

Answer: 18 meters

Explanation:

Length of the rectangle = 5 meter

Width of the rectangle = 4 meters

The perimeter of the rectangle = l + w + l + w

= 5 + 4 + 5 + 4 = 18 meters

Thus the correct answer is option C.

**Spiral Review**

Question 3.

Which is the most reasonable estimate for the measure of the angle Natalie drew?

Options:

a. 30°

b. 90°

c. 180°

d. 210°

Answer: 90°

Explanation:

By seeing the above figure we can say that it is the right angle.

The correct answer is option B.

Question 4.

Ethan has 3 pounds of mixed nuts. How many ounces of mixed nuts does Ethan have?

Options:

a. 30 ounces

b. 36 ounces

c. 48 ounces

d. 54 ounces

Answer: 48 ounces

Explanation:

Given that, Ethan has 3 pounds of mixed nuts.

1 pound = 16 ounces

3 pounds = 3 × 16 ounces = 48 ounces

Therefore the correct answer is option C.

Question 5.

How many lines of symmetry does the shape below appear to have?

Options:

a. 0

b. 1

c. 2

d. more than 2

Answer: 1

Explanation:

The above shape has 1 line of symmetry.

The correct answer is option B.

Question 6.

Which of the following comparisons is correct?

Options:

a. 0.70 > 7.0

b. 0.7 = 0.70

c. 0.7 < 0.70

d. 0.70 = 0.07

Answer: 0.7 = 0.70

Explanation:

a. 0.70 > 7.0

7.0 = 7

0.7 is less than 7

b. 0.7 = 0.70

0.7 is nothing but 0.70

So, the comparision is correct.

The answer is option B.

### Page No. 725

Question 1.

Find the area of the rectangle.

A = _____ square cm

Answer: 143 square cm

Explanation:

Length = 11 cm

Width = 13 cm

Area of the rectangle = l × w

= 11 cm × 13 cm = 143 square cm

Therefore the area of the rectangle = 143 square cm

**Find the area of the rectangle or square.**

Question 2.

A = _____ square inches

Answer: 14 square inches

Explanation:

Length = 7 inches

Width = 2 inches

Area of the rectangle = l × w

= 7 inches × 2 inches = 14 inches

Therefore the area of the rectangle = 14 square inches

Question 3.

A = _____ square meters

Answer: 81 square meters

Explanation:

Side of the square = 9 m

Area of a square = s × s

= 9 m × 9 m = 81 square meters

Thus the area of a square = 81 square meters

Question 4.

A = _____ square feet

Answer: 112 square feet

Explanation:

Length = 8 feet

Width = 14 feet

Area of the rectangle = l × w

= 8 feet × 14 feet = 112 square feet

Therefore, area of the rectangle = 112 square feet

**Find the area of the rectangle or square.**

Question 5.

A = _____ square feet

Answer: 65 square feet

Explanation:

Length of the rectangle = 13 ft

Width of the rectangle = 5 feet

Area of a rectangle = l × w

= 13 feet × 5 feet = 65 square feet

Thus, the area of the rectangle = 65 square feet

Question 6.

A = _____ square yards

Answer: 169 square yards

Explanation:

Side of the square = 13 yards

Area of a square = s × s

= 13 yards × 13 yards = 169 square yards

Therefore, the area of a square = 169 square yards

Question 7.

A = _____ square centimeters

Answer: 40 square centimeters

Explanation:

Length of the rectangle = 20 cm

Width of the rectangle = 2 cm

Area of a rectangle = l × w

= 20 cm × 2 cm = 40 square centimeters

Therefore the area of the rectangle = 40 square centimeters.

**Practice: Copy and Solve Find the area of the rectangle.**

Question 8.

base: 16 feet

height: 6 feet

A = _____ square feet

Answer: 96 square feet

Explanation:

base: 16 feet

height: 6 feet

Area of a rectangle = b ×h

= 16 feet × 6 feet = 96 square feet

Thus the area of the rectangle = 96 square feet

Question 9.

base: 9 yards

height: 17 yards

A = _____ square yards

Answer: 153 square yards

Explanation:

base: 9 yards

height: 17 yards

Area of a rectangle = b × h

9 yards × 17 yards = 153 square yards

The area of the rectangle = 153 square yards

Question 10.

base: 14 centimeters

height: 11 centimeters

A = _____ square centimeters

Answer: 154 square centimeters

Explanation:

base: 14 centimeters

height: 11 centimeters

Area of a rectangle = b × h

14 centimeters × 11 centimeters = 154 square centimeters

The area of the rectangle = 154 square centimeters

Question 11.

Terry’s rectangular yard is 15 meters by 18 meters. Todd’s rectangular yard is 20 meters by 9 meters. How much greater is the area of Terry’s yard than Todd’s yard?

_____ square meters

Answer: 90 square meters

Explanation:

Given,

Terry’s rectangular yard is 15 meters by 18 meters.

Todd’s rectangular yard is 20 meters by 9 meters.

Terry’s rectangular yard:

Area of a rectangle = b × h

= 15 meters × 18 meters = 270 square meters

Todd’s rectangular yard:

Area of a rectangle = b × h

20 meters × 9 meters = 180 square meters

270 square meters – 180 square meters = 90 square meters

Terry’s yard is 90 square meters greater than Todd’s yard.

Question 12.

Reason Quantitatively Carmen sewed a square baby quilt that measures 36 inches on each side. What is the area of the quilt?

A = _____ square inches

Answer: 1296 square inches

Explanation:

Carmen sewed a square baby quilt that measures 36 inches on each side.

Area of a square = s × s

= 36 inches × 36 inches = 1296 square inches

Therefore the area of the quilt is 1296 square inches.

### Page No. 726

Question 13.

Nancy and Luke are drawing plans for rectangular flower gardens. In Nancy’s plan, the garden is 18 feet by 12 feet. In Luke’s plan, the garden is 15 feet by 15 feet. Who drew the garden plan with the greater area? What is the area?

a. What do you need to find?

Type below:

__________

Answer: I need to find who drew the garden plan with the greater area.

Question 13.

b. What formula will you use?

Type below:

__________

Answer: I will Area of rectangle and Area of a square formula

Question 13.

c. What units will you use to write the answer?

Type below:

__________

Answer: Square feet units

Question 13.

d. Show the steps to solve the problem.

Type below:

__________

Answer:

First, we need to find the area of Nancy’s plan

Length = 18 feet

Width = 12 feet

Area of a rectangle = l × w

A = 18 feet × 12 feet = 216 square feet

And now we need to find the area of Luke’s plan

A = s × s

A = 15 feet × 15 feet = 225 square feet

Question 13.

e. Complete the sentences.

The area of Nancy’s garden is _______.

The area of Luke’s garden is _______.

_______ garden has the greater area.

Type below:

__________

Answer:

The area of Nancy’s garden is 216 square feet.

The area of Luke’s garden is 225 square feet.

Luke’s garden has a greater area.

Question 14.

Victor wants to buy fertilizer for his yard. The yard is 35 feet by 55 feet. The directions on the bag of fertilizer say that one bag will cover 1,250 square feet. How many bags of fertilizer should Victor buy to be sure that he covers the entire yard?

______ bags

Answer: 2 bags

Explanation:

Given that,

Victor wants to buy fertilizer for his yard. The yard is 35 feet by 55 feet.

The directions on the bag of fertilizer say that one bag will cover 1,250 square feet.

A = b × h

A = 35 feet × 55 feet

A = 1925 square feet

1925 square feet is greater than 1,250 square feet.

So, Victor has to buy 2 bags to be sure that he covers the entire yard.

Question 15.

Tuan is an artist. He is painting on a large canvas that is 45 inches wide. The height of the canvas is 9 inches less than the width. What is the area of Tuan’s canvas?

A = ______ square inches

Answer: 1620 square inches

Explanation:

Tuan is an artist. He is painting on a large canvas that is 45 inches wide.

The height of the canvas is 9 inches less than the width.

So, h = 45 – 9 = 36 inches

A = b × h

A = 45 inches × 36 inches

A = 1,620 square inches

Therefore the area of Tuan’s canvas is 1620 square inches.

### Common Core – New – Page No. 727

**Area**

**Find the area of the rectangle or square.**

Question 1.

Question 2.

______ square yards

Answer: 64 square yards

Explanation:

Side of the square = 8 yards

Area of the square = s × s

8 yards × 8 yards = 64 square yards

Therefore, The area of the square is 64 square yards.

Question 3.

_____ square meters

Answer: 45 square meters

Explanation:

Length of the rectangle = 15 m

Width of the rectangle = 3 m

Area of the rectangle = b × h

= 15 m × 3 m = 45 square meters

Thus the area of the rectangle is 45 square meters.

Question 4.

______ square inches

Answer: 78 square inches

Explanation:

The base of the rectangle = 13 in.

Height of the rectangle = 6 in.

Area of the rectangle = b × h

13 in. × 6 in. = 78 square inches

Thus the area of the rectangle is 78 square inches.

Question 5.

______ square centimeters

Answer: 150 square centimeters

Explanation:

The base of the rectangle = 30 cm

Height of the rectangle = 5 cm

Area of the rectangle = b × h

30 cm × 5 cm = 150 square centimeters

Therefore, the area of the rectangle = 150 square centimeters

Question 6.

______ square feet

Answer: 56 square feet

Explanation:

The base of the rectangle = 14 feet

Height of the rectangle = 4 feet

Area of the rectangle = b × h

14 feet × 4 feet = 56 square feet

Therefore, the area of the rectangle = 56 square feet.

**Problem Solving**

Question 7.

Meghan is putting wallpaper on a wall that measures 8 feet by 12 feet. How much wallpaper does Meghan need to cover the wall?

______ square feet wallpaper

Answer: 96 square feet

Explanation:

Meghan is putting wallpaper on a wall that measures 8 feet by 12 feet.

The base of the rectangle = 8 feet

Height of the rectangle = 12 feet

Area of the rectangle = b × h

8 feet × 12 feet = 96 square feet

Thus the Area of the rectangle = 96 square feet

Question 8.

Bryson is laying down sod in his yard to grow a new lawn. Each piece of sod is a 1-foot by 1-foot square. How many pieces of sod will Bryson need to cover his yard if his yard measures 30 feet by 14 feet?

______ pieces

Answer: 420 pieces

Explanation:

Bryson is laying down sod in his yard to grow a new lawn.

Each piece of sod is a 1-foot by 1-foot square.

The base of the rectangle = 30 feet

Height of the rectangle = 14 feet

Area of the rectangle = b × h

= 30 feet × 14 feet = 420 sq. ft.

Therefore Bryson needs 420 pieces of sod to cover his yard.

### Common Core – New – Page No. 728

**Lesson Check**

Question 1.

Ellie and Heather drew floor models of their living rooms. Ellie’s model represented 20 feet by 15 feet. Heather’s model represented 18 feet by 18 feet. Whose floor model represents the greater area? How much greater?

Options:

a. Ellie; 138 square feet

b. Heather; 24 square feet

c. Ellie; 300 square feet

d. Heather; 324 square feet

Answer: Heather; 24 square feet

Explanation:

Given,

Ellie and Heather drew floor models of their living rooms.

Ellie’s model represented 20 feet by 15 feet.

Heather’s model represented 18 feet by 18 feet.

Area of Ellie’s model = 20 feet × 15 feet = 300 square feet

Area of Heather’s model = 18 feet × 18 feet = 324 square feet

Now subtract the area of Ellie’s model from Heather’s model = 324 square feet – 300 square feet = 24 square feet

Thus the area of Heather’s model is greater than Ellie’s model

The correct answer is option B.

Question 2.

Tyra is laying down square carpet pieces in her photography studio. Each square carpet piece is 1 yard by 1 yard. If Tyra’s photography studio is 7 yards long and 4 yards wide, how many pieces of square carpet will Tyra need?

Options:

a. 10

b. 11

c. 22

d. 28

Answer: 28

Explanation:

Tyra is laying down square carpet pieces in her photography studio.

Each square carpet piece is 1 yard by 1 yard. Tyra’s photography studio is 7 yards long and 4 yards wide

Area of the rectangle = b × h

= 7 yards × 4 yards

= 28 square yards

Thus the correct answer is option D.

**Spiral Review**

Question 3.

Typically, blood fully circulates through the human body 8 times each minute. How many times does blood circulate through the body in 1 hour?

Options:

a. 48

b. 240

c. 480

d. 4,800

Answer: 480

Explanation:

Blood fully circulates through the human body 8 times each minute.

1 minute = 60 seconds

8 × 60 seconds = 480 seconds

The correct answer is option C.

Question 4.

Each of the 28 students in Romi’s class raised at least $25 during the jump-a-thon. What is the least amount of money the class raised?

Options:

a. $5,200

b. $700

c. $660

d. $196

Answer: $700

Explanation:

Each of the 28 students in Romi’s class raised at least $25 during the jump-a-thon.

Multiply number od students with $25

28 × $25 = $700

The correct answer is option B.

Question 5.

What is the perimeter of the shape below if 1 square is equal to 1 square foot?

Options:

a. 12 feet

b. 14 feet

c. 24 feet

d. 28 feet

Answer: 28 feet

Explanation:

Given that 1 square is equal to 1 square foot

There are 14 squares

Length = 14 squares

Width = 2 squares

Area of the rectangle = l × w = 14 × 2 = 28 sq. feets

The correct answer is option D.

Question 6.

Ryan is making small meat loaves. Each small meat loaf uses \(\frac{3}{4}\) pound of meat. How much meat does Ryan need to make 8 small meat loaves?

Options:

a. 4 pounds

b. 6 pounds

c. 8 pounds

d. 10 \(\frac{2}{3}\) pounds

Answer: 6 pounds

Explanation:

Ryan is making small meatloaves.

Each small meatloaf uses \(\frac{3}{4}\) pound of meat.

Ryan need to make 8 small meatloaves.

\(\frac{3}{4}\) × 8 = 6 pounds

The correct answer is option B.

### Page No. 731

Question 1.

Explain how to find the total area of the figure.

A = ______ square units

Answer: 23 square units

Explanation:

Rectangle:

Each square box = 1 unit

There are 7 units

Base = 7 units

Height = 2 units

The area of the figure = b × h

A = 7 units × 2 units = 14 square units

Square:

The side is 3 units

Area of the square = 3 units × 3 units = 9 square units

Add both the areas = 14 square units + 9 square units = 23 square units

Therefore the area of the above figure is 23 square units.

**Find the area of the combined rectangles.**

Question 2.

A = ______ square mm

Answer: 72 square mm

Explanation:

Area of top rectangle = b × h

Base = 12 mm

Height = 3 mm

A = 12 mm × 3 mm = 36 square mm

Area of square = s × s

s = 6 mm

A = 6 mm × 6 mm = 36 square mm

Area of the figure = 36 square mm + 36 square mm = 72 square mm

Thus the area of the above figure is 72 square mm.

Question 3.

A = ______ square miles

Answer: 146 square miles

Explanation:

Area of rectangle = b × h

Area of the first rectangle = 10 mi × 9 mi

A = 90 square miles

Area of the second rectangle = 8 mi × 7 mi

A = 56 square miles

Area of the figure = Area of first rectangle + Area of the second rectangle

Area of the figure = 90 square mi + 56 square miles

Thus the Area of the figure = 146 square miles

Question 4.

A = ______ square feet

Answer: 96 square feet

Explanation:

There are 2 squares and one rectangle in this figure

Area of the square = s × s

A = 4 ft × 4 ft = 16 square ft

Area of the square = s × s

A = 4 ft × 4 ft = 16 square ft

Area of the rectangle = b × h

A = 16 ft × 4 ft = 64 square ft

Area of the figure = 16 square ft + 16 square ft + 64 square ft

Thus the Area of the figure = 96 square feet.

**Find the area of the combined rectangles.**

Question 5.

Attend to Precision Jamie’s mom wants to enlarge her rectangular garden by adding a new rectangular section. The garden is now 96 square yards. What will the total area of the garden be after she adds the new section?

A = ______ square yards

Answer: 180 square yards

Explanation:

There are 2 rectangles in the above figure

Area of rectangle = b × h

A = 12 yard × 8 yards = 96 square yards

Area of rectangle = b × h

A = 6 yards × 14 yards = 84 square yards

Area of the figure = 96 square yards + 84 square yards

Therefore the area of the figure = 180 square yards.

Question 6.

Explain how to find the perimeter and area of the combined rectangles at the right.

P = ______ feet; A = ______ square feet

Answer: A = 92 square feet; P = 52 feet

Explanation:

There are 2 rectangle in the figure

Area of rectangle = b × h

A = 5 ft × 4 ft = 20 square ft

Area of rectangle = b × h

A = 8 ft × 9 ft = 72 square ft

Area of the figure = 20 square ft + 72 square ft = 92 square ft

Perimeter of the rectangle = 2l + 2w

P = 2 × 5 + 2 × 4 = 10 + 8 = 18 feet

Perimeter of the rectangle = 2l + 2w

P = 2 × 8 + 2 × 9 = 16 + 18 = 34 feet

Perimeter of the figure = 52 feet

### Page No. 732

Question 7.

The diagram shows the layout of Mandy’s garden. The garden is the shape of combined rectangles. What is the area of the garden?

a. What do you need to find?

Type below:

__________

Answer: I need to find the area of the garden.

Question 7.

b. How can you divide the figure to help you find the total area?

Type below:

__________

Answer: I will divide the figure into 3 parts to find the total area

Question 7.

c. What operations will you use to find the answer?

Type below:

__________

Answer: I will use the addition operation to find the area.

Question 7.

d. Draw a diagram to show how you divided the figure. Then show the steps to solve the problem.

Type below:

__________

Answer:

There are 2 rectangles and 1 square in this figure.

Area of rectangle = b × h

Base = 1 ft

H = 7 ft

A = 1 ft × 7 ft = 7 square ft

Area of rectangle = b × h

Base = 5 ft

H = 2 ft

A = 5 ft × 2 ft = 10 square ft

Area of the square = s × s

A = 3 ft × 3 ft = 9 square ft

Total area = 7 square ft + 10 square ft + 9 square ft

= 26 square ft

Question 8.

Workers are painting a large letter L for an outdoor sign. The diagram shows the dimensions of the L. For numbers 8a–8c, select Yes or No to tell whether you can add the products to find the area that the workers will paint.

8a. 2 × 8 and 2 × 4

i. yes

ii. no

Answer: Yes

Explanation:

There are 2 rectangles in the above figure

B = 2 ft

H = 8 ft

A = 2 × 8

B = 4 ft

H = 2 ft

A = 4 × 2

Thus the above statement is correct.

Question 8.

8b. 2 × 6 and 2 × 8

i. yes

ii. no

Answer: No

There are 2 rectangles in the above figure

B = 6 ft

H = 2 ft

A = 2 × 6

Then 2 will be subtracted from 8 = 6

So, the above statement 2 × 6 and 2 × 8 is false.

Question 8.

8c. 2 × 6 and 6 × 2

i. yes

ii. no

Answer: Yes

Explanation:

There are 2 rectangles in the above figure

B = 6 ft

H = 2 ft

A = 6 × 2

B = 2 ft

H = 6 ft

A = 2 × 6

Thus the above statement is true.

### Common Core – New – Page No. 733

**Area of Combined Rectangles**

**Find the area of the combined rectangles.**

Question 1.

Question 2.

______ square feet

Answer: 143 square feet

Explanation:

Area of A = 9 ft × 5 ft = 45 sq. ft.

Area of B = 14 ft. × 7 ft. = 98 sq. ft.

Total Area = Area of A + Area of B

= 45 sq. ft. + 98 sq. ft. = 143 square feet

Therefore the total Area = 143 square feet

Question 3.

______ square inches

Answer: 63 square inches

Explanation:

Area of A = 9 in. × 5 in. = 45 square inches

Area of B = 6 inches × 3 inches = 18 square inches

Total Area = Area of A + Area of B

Total Area = 45 square inches + 18 square inches

Total Area = 63 square inches

Question 4.

______ square feet

Answer: 50 square feet

Explanation:

Area of A = 4 feet × 2 feet = 8 square feet

Area of B = 7 feet × 6 feet = 42 square feet

Total Area = Area of A + Area of B

Total Area = 8 square feet + 42 square feet

Total Area = 50 square feet

Question 5.

______ square centimeters

Answer: 180 square centimeters

Explanation:

Area of A = 12 cm × 7 cm = 84 square cm

Area of B = 16 cm × 6 cm = 96 square cm

Total Area = Area of A + Area of B

Total Area = 84 square cm + 96 square cm

Total Area = 180 square centimeters

Question 6.

______ square yards

Answer: 68 square yards

Explanation:

Area of A = 14 yd × 1 yd = 14 square yards

Area of B = 9 yd × 6 yd = 54 square yards

Total Area = Area of A + Area of B

Total Area = 14 square yards + 54 square yards

Total Area = 68 square yards

**Problem Solving**

**Use the diagram for 7–8.**

**Nadia makes the diagram below to represent the counter space she wants to build in her craft room.**

Question 7.

What is the area of the space that Nadia has shown for scrapbooking?

______ square feet

Answer: 52 square feet

Explanation:

Length = 13 feet

Width = 9 feet – 5 feet = 4 feet

Area of scrapbooking = l × w

= 13 feet × 4 feet

= 52 square feet

Therefore the area of the space that Nadia has shown for scrapbooking is 52 square feet.

Question 8.

What is the area of the space she has shown for painting?

______ square feet

Answer: 25 square feet

Explanation:

The space for painting is a square.

Side of the square is 5 feet

Area of the square = 5 feet × 5 feet

= 25 square feet

Thus the area of the space she has shown for painting is 25 square feet.

### Common Core – New – Page No. 734

**Lesson Check**

Question 1.

What is the area of the combined rectangles below?

Options:

a. 136 square yards

b. 100 square yards

c. 76 square yards

d. 64 square yards

Answer: 76 square yards

Explanation:

Area of 1st rectangle = 5 yards × 8 yards = 40 square yards

Area of 2nd rectangle = 12 yards × 3 yards = 36 square yards

Area of the figure = Area of 1st rectangle + Area of 2nd rectangle

Area of the figure = 40 square yards + 36 square yards

Therefore, the Area of the figure is 76 square yards.

So, the correct answer is option C.

Question 2.

Marquis is redecorating his bedroom. What could Marquis use the area formula to find?

Options:

a. how much space should be in a storage box

b. what length of wood is needed for a shelf

c. the amount of paint needed to cover a wall

d. how much water will fill up his new aquarium

Answer: the amount of paint needed to cover a wall

**Spiral Review**

Question 3.

Giraffes are the tallest land animals. A male giraffe can grow as tall as 6 yards. How tall would the giraffe be in feet?

Options:

a. 2 feet

b. 6 feet

c. 12 feet

d. 18 feet

Answer: 18 feet

Explanation:

Giraffes are the tallest land animals. A male giraffe can grow as tall as 6 yards.

6 yards + 6 yards + 6 yards = 18 yards

The correct answer is option D.

Question 4.

Drew purchased 3 books for $24. The cost of each book was a multiple of 4. Which of the following could be the prices of the 3 books?

Options:

a. $4, $10, $10

b. $4, $8, $12

c. $5, $8, $11

d. $3, $7, $14

Answer: $4, $8, $12

Explanation:

Given that,

Drew purchased 3 books for $24.

The cost of each book was a multiple of 4.

So, the prices of books will be multiple of 4.

That means $4 × 1, $4 × 2, $4 × 3

= $4, $8, $12

The correct answer is option B.

Question 5.

Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long. What is the perimeter of her magnet?

Options:

a. 3 inches

b. 7 inches

c. 9 inches

d. 12 inches

Answer: 12 inches

Explanation:

Esmeralda has a magnet in the shape of a square. Each side of the magnet is 3 inches long.

Side = 3 inches

The perimeter of the square = 4s

P = 4 × 3 = 12 inches

The correct answer is option D.

Question 6.

What is the area of the rectangle below?

Options:

a. 63 square feet

b. 32 square feet

c. 18 square feet

d. 16 square feet

Answer: 63 square feet

Explanation:

Area of the rectangle = base × height

Base = 9 feet

Height = 7 feet

A = 9 feet × 7 feet

A = 63 square feet

Thus the correct answer is option A.

### Page No. 735

**Choose the best term from the box.**

Question 1.

A square that is 1 unit wide and 1 unit long is a ________.

__________

Answer: Square unit

Question 2.

The _______ of a two-dimensional figure can be any side.

__________

Answer: Base

Question 3.

A set of symbols that expresses a mathematical rule is called a ______.

__________

Answer: Formula

Question 4.

The ______ is the distance around a shape.

__________

Answer: Perimeter

**Find the perimeter and area of the rectangle or square.**

Question 5.

Perimeter = ______ cm

Area = ______ square cm

Answer:

Perimeter = 52 cm

Area = 169 square cm

Explanation:

P = 4s

P = 4 × 13 = 52 cm

A = s × s

A = 13 × 13 = 169 square cm

Question 6.

Perimeter = ______ ft

Area = ______ square ft

Answer:

Perimeter: 48 ft

Area = 63 square ft

Explanation:

Base = 21 ft

Height = 3 ft

P = 2l +2w

P = 2 (21 ft + 3 ft)

P = 2 × 24 = 48 feet

A = b × h

A = 21 × 3

A = 63 square ft

Question 7.

Perimeter = ______ in.

Area = ______ square in.

Answer:

Perimeter = 46 in.

Area = 120 square in.

Explanation:

P = 2l +2w

P = 2 × 15 + 2 × 8

P = 30 + 16 = 46 inches

A = l × w

A = 15 × 8 = 120 square inches

Question 8.

Area = ____ square yd

Answer:

Area of the rectangle = 20 yards × 5 yards = 100 square yards

Area of the rectangle = 18 yards × 5 yards = 90 square yards

Area of the figure = 100 square yards + 90 square yards = 190 square yards

Question 9.

Area = ____ square meters

Answer:

A = b × h

A = 5 m × 2 m = 10 square meters

A = b × h

A = 5 m × 2 m = 10 square meters

A = b × h

A = 4 m × 2 m = 8 square meters

Now add all the areas

10 square meters + 10 square meters + 8 square meters

= 28 square meters

Therefore the area of the figures is 28 square meters

Question 10.

Area = ____ square feet

Answer:

Area of the rectangle = b × h

A = 14 ft × 2 ft = 28 square feet

A = s × s

A = 8 ft × 8 ft = 64 square feet

Area of the figures = 64 square feet + 28 square feet

Therefore Area of the figure = 92 square feet

### Page No. 736

Question 11.

Which figure has the greatest perimeter?

________

Answer: Figure B has the highest perimeter.

Explanation:

P = 2l +2w

P = 2 × 3 + 2 ×5 = 6 + 10 = 16

P = 2 × 6 + 2 × 3 = 12 + 6 = 18

P = 4a = 4 × 4 = 16

P = 2 × 4 + 2 × 3 = 8+ 6 = 14

Thus the greatest perimeter is figure B.

Question 12.

Which figure has an area of 108 square centimeters?

________

Answer: Figure C

Explanation:

A = 13 cm × 6 cm = 78 square cm.

A = 11 cm × 11 cm = 121 square cm.

A = 12 cm × 9 cm = 108 square cm.

A = 16 cm × 38 cm = 608 square cm.

Thus the area of 108 square centimeters is Figure C.

Question 13.

Which of the combined rectangles has an area of 40 square feet?

________

Answer: Figure A

Explanation:

Area of top rectangle = 6 ft × 2 ft = 12 square feet

Area of bottom rectangle = 6 ft × 2 ft = 12 square feet

Area of square = 4 ft × 4 ft = 16 square feet

Add Area of top rectangle, Area of bottom rectangle and Area of square

= 12 square feet + 12 square feet + 16 square feet = 40 square feet.

Thus the correct answer is option A.

### Page No. 739

Question 1.

Find the unknown measure. The area of the rectangle is 36 square feet.

A = b × h

The base of the rectangle is ________ .

base = _____ ft

Answer: 12 feet

Explanation:

Given,

The area of the rectangle = 36 square feet

Height = 3 feet

Base =?

A = b × h

36 square feet = b × 3 feet

b × 3 feet = 36 square feet

b = 36/3 = 12 feet

The base of the rectangle is 12 feets.

**Find the unknown measure of the rectangle.**

Question 2.

Perimeter = 44 centimeters

width = _____ cm

Answer: 10 cm

Explanation:

Given,

Perimeter = 44 centimeters

Length = 12 cm

width =?

The perimeter of the rectangle = 2 (l + w)

P = 2l + 2w

44 cm = 24 cm + 2w

2w = 44 cm – 24 cm

2w = 20 cm

w = 20/2 = 10

Therefore width = 10 cm

Question 3.

Area = 108 square inches

height = _____ in.

Answer: 12 inches

Explanation:

Given,

Area = 108 square inches

Base = 9 inches

height = _____ in.

A = b × h

108 square inches = 9 inches × h

h = 108/9

Height = 12 inches

Therefore the height of the rectangle = 12 inches

Question 4.

Area = 90 square meters

base = _____ cm

Answer: 18 meters

Explanation:

Given,

Area = 90 square meters

Height = 5 meters

base = _____ cm

A = b × h

90 square meters = b × 5 meters

b × 5 meters = 90 square meters

b = 90/5 = 18 meters

Therefore the base of the rectangle = 18 meters

Question 5.

Perimeter = 34 yards

length = _____ yd

Answer: 12 yards

Explanation:

Given,

Perimeter = 34 yards

Width = 5 yards

Length =?

The perimeter of the rectangle = 2 (l + w)

P = 2l + 2w

34 yards = 2 × l + 2 × 5 yards

34 yards = 2 × l + 10 yards

2 × l + 10 yards = 34 yards

2l = 34 yards – 10 yards

2l = 24 yards

l = 24/2 = 12 yards

Therefore the length of the rectangle = 12 yards.

Question 6.

Area = 96 square feet

base = ______ ft

Answer: 12 feet

Explanation:

Given,

Area = 96 square feet

Height = 8 feet

Base =?

A = b × h

96 square feet = b × 8 feet

b × 8 feet = 96 square feet

b = 96/8 = 12 feet

Thus base of the rectangle = 12 feet.

Question 7.

Area = 126 square centimeters

height = _____ centimeters

Answer: 14 centimeters

Explanation:

Given,

Area = 126 square centimeters

Base = 9 cm

height = _____ centimeters

A = b × h

126 square centimeters = 9 cm × h

9 cm × h = 126 square centimeters

h = 126/9 = 14 centimeters

Therefore the Height of the rectangle = 14 centimeters

Question 8.

A square has an area of 49 square inches. Explain how to find the perimeter of the square.

Type below:

________

Answer:

Explanation:

Given that,

A square has an area of 49 square inches.

A = 49 square inches

s^2 = 49 square inches

The square root of 49 is 7

So, each side of the square is 7 inches

The perimeter of the square = 4 × s

4 × 7 inches = 28 inches.

Therefore the perimeter of the square is 28 inches.

### Page No. 740

Question 9.

Identify Relationships The area of a swimming pool is 120 square meters. The width of the pool is 8 meters. What is the length of the pool in centimeters?

length = _____ centimeters

Answer:

Given that the area of a swimming pool is 120 square meters.

The width of the pool is 8 meters.

We have to find the length of the pool in centimeters.

We know that Area of the rectangle = l × w

A = l × w

120 square meters = l × 8 meters

l × 8 meters = 120 square meters

l = 120/8 = 15 meters

Therefore, the length of the pool = 15 meters

Convert meters to centimeters

1 meter = 100 centimeters

15 meters = 1500 centimeters.

The length of the pool in centimeters = 1500 centimeters

Question 10.

An outdoor deck is 7 feet wide. The perimeter of the deck is 64 feet. What is the length of the deck? Use the numbers to write an equation and solve. A number may be used more than once.

P=(2 × l) + (2 × w)

So, the length of the deck is _______ feet.

length = _____ ft

Answer:

An outdoor deck is 7 feet wide.

The perimeter of the deck is 64 feet.

We know that,

P=(2 × l) + (2 × w)

64 feet = (2 × l) + (2 × 7)

64 feet = 2l + 14 feet

2 × l = 64 feet – 14 feet

2 × l = 50 feet

l = 50/2 = 25 feet

Therefore the length of the deck = 25 feet.

Question 11.

A male mountain lion has a rectangular territory with an area of 96 square miles. If his territory is 8 miles wide, what is the length of his territory?

length = _____ miles

Answer:

A male mountain lion has a rectangular territory with an area of 96 square miles.

Width = 8 miles

Length =?

A = l × w

96 square miles = l × 8 miles

l × 8 miles = 96 square miles

l = 96/8

l = 12 miles

Therefore, length of his territory = 12 miles

### Common Core – New – Page No. 741

**Find Unknown Measures**

**Find the unknown measure of the rectangle.**

Question 1.

Perimeter = 54 feet

width = 7 feet

Think: P = (2 × l) + (2 × w)

54 = (2 × 20) + (2 × w)

54 = 40 + (2 × w)

Since 54 = 40 + 14, 2 × w = 14, and w = 7.

Question 2.

Perimeter = 42 meters

length = _____ meters

Answer: length = 12 meters

Explanation:

Given, Perimeter = 42 meters

Width = 9 meters

P = (2 × l) + (2 × w)

P = (2 × l) + (2 × 9 m)

42 m = 2l + 18 m

42 m – 18 m = 2l

2l = 24 meters

l = 24 meters/2 = 12 meters

Therefore length = 12 meters

Question 3.

Area = 28 square centimeters

height = _____ centimeters

Answer: height = 7 centimeters

Explanation:

Given,

Area = 28 square centimeters

Base = 4 cm

A = b × h

28 square centimeters = 4 cm × h

4 × h = 28

h = 28/4 = 7 cm

The height of the rectangle = 7 centimeters

Question 4.

Area = 200 square inches

base = _____ inches

Answer: base = 8 inches

Explanation:

Given,

Area = 200 square inches

Height = 25 inches

Base = ?

Area of the rectangle = b × h

200 square inches = b × 25 inches

b × 25 inches = 200 square inches

b = 200/25 = 8 inches

The base of the rectangle = 8 inches.

**Problem Solving**

Question 5.

Susie is an organic vegetable grower. The perimeter of her rectangular vegetable garden is 72 yards. The width of the vegetable garden is 9 yards. How long is the vegetable garden?

length = _____ yards

Answer: 27 yards

Explanation:

Susie is an organic vegetable grower.

The perimeter of her rectangular vegetable garden is 72 yards.

The width of the vegetable garden is 9 yards.

P = 72 yards

W = 9 yards

L =?

We know that,

P = (2 × l) + (2 × w)

72 yards = (2 × l) + (2 × 9)

72 yards – 18 yards = (2 × l)

(2 × l) = 72 yards – 18 yards

2l = 54 yards

l = 54/2 = 27 yards

Thus the vegetable garden is 27 yards long.

Question 6.

An artist is creating a rectangular mural for the Northfield Community Center. The mural is 7 feet tall and has an area of 84 square feet. What is the length of

the mural?

length = _____ feet

Answer: 12 feet

Explanation:

An artist is creating a rectangular mural for the Northfield Community Center.

The mural is 7 feet tall and has an area of 84 square feet.

A = 84 square feet

W = 7 feet

L =?

A = l × w

84 square feet = l × 7 feet

l × 7 feet = 84 square feet

l = 84/7 = 12 feet

Thus the length of Murali is 12 feet.

### Common Core – New – Page No. 742

**Lesson Check**

Question 1.

The area of a rectangular photograph is 35 square inches. If the width of the photo is 5 inches, how tall is the photo?

Options:

a. 5 inches

b. 7 inches

c. 25 inches

d. 30 inches

Answer: 7 inches

Explanation:

The area of a rectangular photograph is 35 square inches.

Width = 5 inches

A = l × w

35 square inches = l × 5 inches

Length = 35/5 = inches

Thus the photo is 7 inches tall.

The correct answer is option B.

Question 2.

Natalie used 112 inches of blue yarn as a border around her rectangular bulletin board. If the bulletin board is 36 inches wide, how long is it?

Options:

a. 20 inches

b. 38 inches

c. 40 inches

d. 76 inches

Answer: 20 inches

Explanation:

Natalie used 112 inches of blue yarn as a border around her rectangular bulletin board.

Width = 36 inches

A = 112 inches

A = l × w

112 inches = l × 36 inches

l × 36 inches = 112 inches

l = 112/36 = 20 inches

Length = 20 inches

The correct answer is option A.

**Spiral Review**

Question 3.

A professional basketball court is in the shape of a rectangle. It is 50 feet wide and 94 feet long. A player ran one time around the edge of the court. How far did the player run?

Options:

a. 144 feet

b. 194 feet

c. 238 feet

d. 288 feet

Answer: 288 feet

Explanation:

A professional basketball court is in the shape of a rectangle.

It is 50 feet wide and 94 feet long.

A player ran one time around the edge of the court.

P = (2 × l) + (2 × w)

P = (2 × 94 feet) + (2 × 50 feet)

P = 188 feet + 100 feet = 288 feet

Therefore the perimeter of the rectangle is 288 feet.

Question 4.

On a compass, due east is a \(\frac{1}{4}\) turn clockwise from due north. How many degrees are in a \(\frac{1}{4}\) turn?

Options:

a. 45°

b. 60°

c. 90°

d. 180°

Answer: 90°

Explanation:

On a compass, due east is a \(\frac{1}{4}\) turn clockwise from due north.

\(\frac{1}{4}\) × 360° = 360°/4 = 90°

The correct answer is option C.

Question 5.

Hakeem’s frog made three quick jumps. The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters. What was the total length of the frog’s three jumps?

Options:

a. 189 centimeters

b. 225 centimeters

c. 486 centimeters

d. 585 millimeters

Answer: 225 centimeters

Explanation:

Hakeem’s frog made three quick jumps.

The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters.

Convert other units to centimeters

1 meter = 100 centimeters

400 millimeters = 40 centimeters

100 + 85 + 40 = 225 centimeters

Thus the correct answer is option B.

Question 6.

Karen colors in squares on a grid. She colored \(\frac{1}{8}\) of the squares blue and \(\frac{5}{8}\) of the squares red. What fraction of the squares are not colored in?

Options:

a. \(\frac{1}{8}\)

b. \(\frac{1}{4}\)

c. \(\frac{1}{2}\)

d. \(\frac{3}{4}\)

Answer: \(\frac{1}{4}\)

Explanation:

Karen colors in squares on a grid.

She colored \(\frac{1}{8}\) of the squares blue and \(\frac{5}{8}\) of the squares red.

\(\frac{1}{8}\) + \(\frac{5}{8}\) = \(\frac{6}{8}\)

Total number of fractions = \(\frac{8}{8}\)

\(\frac{8}{8}\) – \(\frac{6}{8}\) = \(\frac{2}{8}\)

\(\frac{1}{4}\) fraction of the squares are not colored.

### Page No. 745

Question 1.

Lila is wallpapering one wall of her bedroom, as shown in the diagram. She will cover the whole wall except for the doorway. How many square feet of wall does Lila need to cover?

First, find the area of the wall.

A = b × h

A_{wall} = _____ square feet

Answer:

Base = 12 feet

Height = 8 feet

A = b × h

A_{wall} = 12 feet × 8 feet

A_{wall} = 96 square feet

Question 1.

Next, find the area of the door.

A = b × h

A_{door} = _____ square feet

Answer:

Base = 3 feet

Height = 7 feet

A = b × h

A_{door} = 3 feet × 7 feet

A_{door} = 21 square feet

Question 1.

Last, subtract the area of the door from the area of the wall.

_____ – _____ = _____ square feet

So, Lila needs to cover _____ of wall.

Type below:

________

Answer:

A_{door} = 21 square feet

A_{wall} = 96 square feet

Last, subtract the area of the door from the area of the wall.

A = A_{wall} – A_{door}

A = 96 square feet – 21 square feet

A = 75 square feet

So, Lila needs to cover 75 square feet

Question 2.

What if there was a square window on the wall with a side length of 2 feet? How much wall would Lila need to cover then? Explain.

______ square feet

Answer:

If there is a square window of length 2 feet

Area of square = s × s

A_{window }= 2 × 2 = 4 square feet

Now Subtract the area of the door, area of the window from the area of the wall.

A = 96 square feet – 21 square feet – 4 square feet

A = 71 square feet

Therefore Lila need to cover 71 square feet.

Question 3.

Ed is building a model of a house with a flat roof, as shown in the diagram. There is a chimney through the roof. Ed will cover the roof with square tiles. If the area of each tile is 1 square inch, how many tiles will he need? Explain.

_____ tiles

Answer:

Roof:

Base = 20 inches

Height = 30 inches

Area of the roof = b × h

A_{roof }= 20 inches × 30 inches

A_{roof }= 600 inches

Chimney:

Base = 3 inches

Height = 4 inches

Area of the chimney = b × h

A_{chimney }= 3 × 4 = 12 inches

Now subtract Area of Chimney from Area of the roof

A = 600 inches – 12 inches

A = 588 inches

Therefore Ed needs 588 tiles.

### Page No. 746

Question 4.

Make Sense of Problems Lia has a dog and a cat. Together, the pets weigh 28 pounds. The dog weighs 3 times as much as the cat. How much does each pet weigh?

cat weight = _____ pounds dog weight = _____ pounds

Answer:

Given that, the pets weigh 28 pounds.

28 = 7 + 7 + 7 + 7

The dog weighs 3 times as much as the cat.

= 3 × 7 = 21 pounds

The dog weighs 21 pounds

28 – 21 = 7

The cat weighs = 7 pounds.

Question 5.

Mr. Foster is covering two rectangular pictures with glass. One is 6 inches by 4 inches and the other one is 5 inches by 5 inches. Does he need the same number of square inches of glass for each picture? Explain.

_____

Answer: No

Explanation:

Mr. Foster is covering two rectangular pictures with glass.

One is 6 inches by 4 inches and the other one is 5 inches by 5 inches.

Area of first rectangular picture = 6 × 4 = 24 square inches

Area of second rectangular picture = 5 × 5 = 25 square inches

Area of two rectangular pictures = 25 square inches – 24 square inches

1 square inch.

Therefore, he doesn’t need the same number of square inches of glass for each picture.

Question 6.

Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter. Is she correct? Explain.

_____

Answer: No

Explanation:

Claire says the area of a square with a side length of 100 centimeters is greater than the area of a square with a side length of 1 meter.

Her statement is not correct because 1 meter = 100 centimeters.

So, the area of a square with a side length of 100 centimeters is equal to the area of a square with a side length of 1 meter.

Question 7.

A rectangular floor is 12 feet long and 11 feet wide. Janine places a rug that is 9 feet long and 7 feet wide and covers part of the floor in the room. Select the word(s) to complete the sentence.

To find the number of square feet of the floor that is NOT covered by the rug,

the the area of the floor.

_____ square feet

Answer:

Length = 12 feet

Width = 11 feet

Area of the rectangular floor = l × w

= 12 feet × 11 feet = 132 square feet

Room:

Length = 9 feet

Width = 7 feet

Area of the floor in the room = l × w

= 9 feet × 7 feet

= 63 square feet

Subtract the area of the rug from the area of the floor

= 132 square feet – 63 square feet = 69 square feet

The number of square feet of the floor that is NOT covered by the rug is 69 square feet.

### Common Core – New – Page No. 747

**Problem Solving Find the Area**

**Solve each problem.**

Question 1.

A room has a wooden floor. There is a rug in the center of the floor. The diagram shows the room and the rug. How many square feet of the wood floor still shows?

82 square feet

Area of the floor: 13 × 10 = 130 square feet

Area of the rug: 8 × 6 = 48 square feet

Subtract to find the area of the floor still showing: 130 – 48 = 82 square feet

Question 2.

A rectangular wall has a square window, as shown in the diagram.

What is the area of the wall NOT including the window?

The area of the wall NOT including the window = _____ square feet

Answer: 96 square feet

Explanation:

Wall:

Base = 14 feet

Height = 8 feet

Area of the wall = b × h

A = 14 feet × 8 feet

A = 112 square feet

Window:

Length = 4 feet

Area of the square = s × s

Area of the window = 4 feet × 4 feet = 16 square feet

Now subtract Area of the window from the area of the rectangular wall

= 112 square feet – 16 square feet

= 96 square feet

Therefore the area of the wall NOT including the window = 96 square feet.

Question 3.

Bob wants to put down new sod in his backyard, except for the part set aside for his flower garden. The diagram shows Bob’s backyard and the flower garden.

How much sod will Bob need?

The area covered with new sod = _____ square yards

Answer: 235 square yards

Flower Garden:

Base = 20 yards

Height = 14 yards

Area of the rectangular flower garden = b × h

A = 20 yards × 14 yards

A = 280 square yards

Sod:

Base = 5 yards

Height = 9 yards

Area of sod = b × h

= 5 yards × 9 yards = 45 square yards

Now subtract area of sod from area of flower garden

= 280 square yards – 45 square yards

= 235 square yards

Thus the area covered with new sod = 235 square yards

Question 4.

A rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting?

The area of the frame = _____ square inches

Answer: 192 square inches

Explanation:

A rectangular painting is 24 inches wide and 20 inches tall without the frame.

A = b × h

A = 24 inches × 20 inches

A = 480 square inches

With the frame, it is 28 inches wide and 24 inches tall.

A = b × h

A = 28 inches × 24 inches

A = 672 square inches

The area of the frame not covered by the painting

= 672 square inches – 480 square inches

= 192 square inches

Therefore, The area of the frame = 192 square inches

Question 5.

One wall in Jeanne’s bedroom is 13 feet long and 8 feet tall. There is a door 3 feet wide and 6 feet tall. She has a poster on the wall that is 2 feet wide and 3 feet tall. How much of the wall is visible?

The area of the wall visible = _____ square feet

Answer: 80 square feet

Explanation:

One wall in Jeanne’s bedroom is 13 feet long and 8 feet tall.

Area of Jeanne’s bedroom = 13 feet × 8 feet = 104 square feet

Area of door = 3 feet × 6 feet = 18 square feet

Area of the wall = 2 feet × 3 feet = 6 square feet

To find the area of the wall visible we have to subtract Area of the wall, Area of the door from Area of Jeanne’s bedroom.

104 square feet – 18 square feet – 6 square feet

= 80 square feet

The area of the wall visible = 80 square feet

### Common Core – New – Page No. 748

**Lesson Check**

Question 1.

One wall in Zoe’s bedroom is 5 feet wide and 8 feet tall. Zoe puts up a poster of her favorite athlete. The poster is 2 feet wide and 3 feet tall. How much of the wall is not covered by the poster?

Options:

a. 16 square feet

b. 34 square feet

c. 35 square feet

d. 46 square feet

Answer: 34 square feet

Explanation:

One wall in Zoe’s bedroom is 5 feet wide and 8 feet tall.

Area of the wall in Zoe’s bedroom = b × h

A = 5 feet × 8 feet

A = 40 square feet

Zoe puts up a poster of her favorite athlete. The poster is 2 feet wide and 3 feet tall.

Area of the poster = b × h

A = 2 feet × 3 feet = 6 square feet

Now subtract Area of the poster from the Area of the wall in Zoe’s bedroom

= 40 square feet – 6 square feet

= 34 square feet

Thus the area of the wall is not covered by the poster = 34 square feet.

The correct answer is option B.

Question 2.

A garage door is 15 feet wide and 6 feet high. It is painted white, except for a rectangular panel 1 foot high and 9 feet wide that is brown. How much of the garage door is white?

Options:

a. 22 square feet

b. 70 square feet

c. 80 square feet

d. 81 square feet

Answer: 81 square feet

Explanation:

A garage door is 15 feet wide and 6 feet high.

Area of the garage door = b × h

A = 15 feet × 6 feet

A = 90 square feet

It is painted white, except for a rectangular panel 1 foot high and 9 feet wide that is brown.

b = 9 feet

h = 1 foot

A = b × h

A = 9 feet × 1 feet

A = 9 square feet

Area of the garage door is white = 90 square feet – 9 square feet

Area of the garage door is white = 81 square feet

The correct answer is option D.

**Spiral Review**

Question 3.

Kate baked a rectangular cake for a party. She used 42 inches of frosting around the edges of the cake. If the cake was 9 inches wide, how long was the cake?

Options:

a. 5 inches

b. 12 inches

c. 24 inches

d. 33 inches

Answer: 12 inches

Explanation:

Kate baked a rectangular cake for a party. She used 42 inches of frosting around the edges of the cake.

Width = 9 inches

P = (2 × l) + (2 × w)

42 inches = (2 × l) + (2 × 9)

(2 × l) + (2 × 9) = 42 inches

(2 × l) = 42 inches – 18 inches

2l = 24 inches

l = 24/2 = 12 inches

Therefore the cake is 12 inches long.

Thus the correct answer is option B.

Question 4.

Larry, Mary, and Terry each had a full glass of juice. Larry drank \(\frac{3}{4}\) of his. Mary drank \(\frac{3}{8}\) of hers. Terry drank \(\frac{7}{10}\) of his. Who drank less than \(\frac{1}{2}\) of their juice?

Options:

a. Larry

b. Mary

c. Mary and Terry

d. Larry and Terry

Answer: Mary

Explanation:

Larry, Mary, and Terry each had a full glass of juice.

Larry drank \(\frac{3}{4}\), Mary drank \(\frac{3}{8}\) and Terry drank \(\frac{7}{10}\) of \(\frac{1}{2}\)

\(\frac{3}{8}\) is less than \(\frac{1}{2}\) of their juice.

The correct answer is Option B.

Question 5.

Which of the following statements is NOT true about the numbers 7 and 9?

Options:

a. 7 is a prime number.

b. 9 is a composite number.

c. 7 and 9 have no common factors other than 1.

d. 27 is a common multiple of 7 and 9.

Answer: 27 is a common multiple of 7 and 9

Explanation:

a. 7 is a prime number is true.

b. 9 is a composite number is true

c. 7 and 9 have no common factors other than 1 is true.

d. 27 is a common multiple of 7 and 9 is not true because 7 is not the multiple of 27.

Thus the correct answer is option D.

Question 6.

Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M. How long did the movie last?

Options:

a. 1 hour 35 minutes

b. 1 hour 45 minutes

c. 1 hour 55 minutes

d. 2 hours 15 minutes

Answer: 1 hour 45 minutes

Explanation:

Tom and some friends went to a movie. The show started at 2:30 P.M. and ended at 4:15 P.M.

Subtract 2:30 P.M. from 4:15 P.M.

4 hour 15 minutes

-2 hour 30 minutes

1 hour 45 minutes

The movie last for 1 hour 45 minutes

Thus the correct answer is option B.

### Page No. 749

Question 1.

For numbers 1a–1e, select Yes or No to indicate if a rectangle with the given dimensions would have a perimeter of 50 inches.

a. length: 25 inches; width: 2 inches

i. yes

ii. no

Answer: No

Explanation:

P = (2 × l) + (2 × w)

50 inches = (2 × 25 in.) + (2 × w)

(2 × w) = 50 inches – 50 inches

w = 0

Thus the above statement is false

Question 1.

b. length: 20 inches; width: 5 inches

i. yes

ii. no

Answer: Yes

Explanation:

P = (2 × l) + (2 × w)

50 inches = (2 × 20 in.) + (2 × 5)

50 inches = 40 in. + 10 in.

Thus the above statement is true.

Question 1.

c. length: 17 inches; width: 8 inches

i. yes

ii. no

Answer: Yes

Explanation:

P = (2 × l) + (2 × w)

50 inches = (2 × 17 in.) + (2 × 8 in.)

50 inches = 34 in. + 16 in.

Thus the above statement is true.

Question 1.

d. length: 15 inches; width: 5 inches

i. yes

ii. no

Answer: No

Explanation:

P = (2 × l) + (2 × w)

50 inches = (2 × 15 in.) + (2 × 5 in.)

50 inches = 30 in. + 10 in.

50 inches = 40 inches

Thus the above statement is false.

Question 1.

e. length: 15 inches; width: 10 inches

i. yes

ii. no

Answer: Yes

Explanation:

P = (2 × l) + (2 × w)

50 inches = (2 × 15 in.) + (2 × 10 in.)

50 inches = 30 in. + 20 in.

50 inches = 50 inches

Thus the above statement is true.

Question 2.

The swimming club’s indoor pool is in a rectangular building.

Marco is laying tile around the rectangular pool.

Part A

What is the area of the pool and the area of the pool and the walkway? Show your work.

A(pool) = ____ m^{2 }A(building) = ____ m^{2}

Answer:

Pool:

Base = 20 m

Height = 16 m

A = b × h

Area of the pool = 20 m × 16 m = 320 square meters

Pool and the walkway:

Area of the pool and the walkway = 26 m × 22 m = 572 square meters

Question 2.

Part B

How many square meters of tile will Marco need for the walkway?

Explain how you found your answer.

A(walkway) = ____ m^{2}

Answer: 252 square meters

Explanation:

Area of walkway = Area of the pool and the walkway – Area of pool

Area of the walkway = 572 square meters – 320 square meters

= 252 square meters

Therefore the Area of walkway = 252 square meters

### Page No. 750

Question 3.

Match the dimensions of the rectangles in the top row with the correct area or perimeter in the bottom row

Answer:

Question 4.

Kyleigh put a large rectangular sticker on her notebook. The height of the sticker measures 18 centimeters. The base is half as long as the height. What area of the notebook does the sticker cover?

________ square centimeters

Answer: 162 square centimeters

Explanation:

Kyleigh put a large rectangular sticker on her notebook.

The height of the sticker measures 18 centimeters.

The base is half as long as the height.

Base = h/2 = 18/2 = 9 centimeters

Area of the rectangle = b × h

A = 9 cm × 18 cm

A = 162 square centimeters

Thus the area of the notebook the sticker cover is 162 square centimeters.

Question 5.

A rectangular flower garden in Samantha’s backyard has 100 feet around its edge. The width of the garden is 20 feet. What is the length of the garden? Use the numbers to write an equation and solve. A number may be used more than once.

□ = (2 × l) + (2 × □)

□ = 2 × l + □

□ = 2 × l

□ = l

So, the length of the garden _____ feet.

Answer:

P = (2 × l) + (2 × w)

100 = (2 × l) + (2 × 20)

100 – 40 = 2 × l

2 × l = 60

l = 60/2 = 30 feet

Length = 30 feet

So, the length of the garden 30 feet.

Question 6.

Gary drew a rectangle with a perimeter of 20 inches. Then he tried to draw a square with a perimeter of 20 inches.

Draw 3 different rectangles that Gary could have drawn. Then draw the square, if possible.

Type below:

__________

Answer:

The possible rectangles with a perimeter of 20 inches are:

The possible square with a perimeter of 20 inches is:

### Page No. 751

Question 7.

Ami and Bert are drawing plans for rectangular vegetable gardens. In Ami’s plan, the garden is 13 feet by 10 feet. In Bert’s plan, the garden is 12 feet by 12 feet. For numbers 7a−7d, select True or False for each statement.

a. The area of Ami’s garden is 130 square feet.

i. True

ii. False

Answer: True

Explanation:

A = b × h

Area of Ami’s garden = 13 feet × 10 feet =

Area of Ami’s garden = 130 square feet

The above statement is true.

Question 7.

b. The area of Bert’s garden is 48 square feet.

i. True

ii. False

Answer: False

Explanation:

Area of Bert’s garden = 12 feet × 12 feet = 144 square feet

The above statement is false.

Question 7.

c. Ami’s garden has a greater area than Bert’s garden.

i. True

ii. False

Answer: False

Explanation:

Area of Ami’s garden = 13 feet × 10 feet = 130 square feet

Area of Bert’s garden = 12 feet × 12 feet = 144 square feet

130 square feet is less than 144 square feet

The area of Ami’s garden is less than Area of Bert’s garden.

The above statement is false.

Question 7.

d. The area of Bert’s garden is 14 square feet greater than Ami’s.

i. True

ii. False

Answer: True

Explanation:

Area of Ami’s garden = 13 feet × 10 feet = 130 square feet

Area of Bert’s garden = 12 feet × 12 feet = 144 square feet

144 square feet – 130 square feet = 14 square feet

The above statement is true.

Question 8.

A farmer planted corn in a square field. One side of the field measures 32 yards. What is the area of the cornfield? Show your work.

_______ square yards

Answer: 1024 square yards

Explanation:

A farmer planted corn in a square field. One side of the field measures 32 yards.

Area of the square = 32 yards × 32 yards

A = 1,024 square yards

Therefore the area of the cornfield is 1,024 square yards.

Question 9.

Harvey bought a frame in which he put his family’s picture.

What is the area of the frame not covered by the picture?

_______ square inches

Answer: 136 square inches

Explanation:

Area of the picture = 12 in. × 18 in.

A = 216 square inches

Area of the frame = 16 in. × 22 in.

A = 352 square inches

The area of the frame not covered by the picture = 352 square inches – 216 square inches

= 136 square inches

Therefore the area of the frame not covered by the picture is 136 square inches.

Question 10.

Kelly has 236 feet of fence to use to enclose a rectangular space for her dog. She wants the width to be 23 feet. Draw a rectangle that could be the space for Kelly’s dog. Label the length and width.

Type below:

________

Answer:

Kelly has 236 feet of fence to use to enclose a rectangular space for her dog.

She wants the width to be 23 feet.

Perimeter = (2 × l) + (2 × w)

236 = (2 × l) + (2 × w)

236 = (2 × l) + (2 × 23)

236 – 46 = (2 × l)

(2 × l) = 190

l = 190/2

l = 95 feet

Therefore length = 95 feet.

### Page No. 752

Question 11.

The diagram shows the dimensions of a new parking lot at Helen’s Health Food store.

Use either addition or subtraction to find the area of the parking lot. Show your work.

_______ square yards

Answer: 1100 square yards

Explanation:

Addition:

Top:

Base = 40 yards

Height = 20 yards

Area of the top rectangle = b × h

A = 40 yards × 20 yards = 800 square yards

Bottom:

Base = 30 yards

Height = 10 yards

Area of the rectangle = b × h

A = 30 yards × 10 yards = 300 square yards

Area of the parking = Area of top + Area of bottom

A = 800 square yards + 300 square yards

Area of parking = 1100 square yards.

Question 12.

Chad’s bedroom floor is 12 feet long and 10 feet wide. He has an area rug on his floor that is 7 feet long and 5 feet wide. Which statement tells how to find the amount of the floor that is not covered by the rug? Mark all that apply.

Options:

a. Add 12 × 10 and 7 × 5.

b. Subtract 35 from 12 × 10

c. Subtract 10 × 5 from 12 × 7.

d. Add 12 + 10 + 7 + 5.

e. Subtract 7 × 5 from 12 × 10.

f. Subtract 12 × 10 from 7 × 5.

Answer: B, F

Chad’s bedroom floor is 12 feet long and 10 feet wide.

A = 12 feet × 10 feet = 120 square feet

Area rug on his floor = 7 feet × 5 feet = 35 square feet

To find the amount of the floor that is not covered by the rug we have to subtract 120 square feet from 35 square feet or 35 square feet from 12 × 10.

So, the correct answers are B and F.

Question 13.

A row of plaques covers 120 square feet of space along a wall. If the plaques are 3 feet tall, what length of the wall do they cover?

____ feet

Answer: 40 feet

Explanation:

Given that,

A row of plaques covers 120 square feet of space along a wall.

Height = 3 feet

A = b × h

120 square feet = b × 3 feet

b = 120/3 = 40

Therefore the base is 40 feet.

### Page No. 753

Question 14.

Ms. Bennett wants to buy carpeting for her living room and dining room.

Explain how she can find the amount of carpet she needs to cover the floor in both rooms. Then find the amount of carpet she will need.

____ square feet

Answer:

She can find the area of each rectangle and then find the sum. The area of the living room is 20 × 20 = 400 square feet.

The area of the dining room is 15 × 10 = 150 square feet.

The sum of the two rooms = 400 + 150 = 550 square feet.

She needs 550 square feet of carpeting.

Question 15.

Lorenzo built a rectangular brick patio. He is putting a stone border around the edge of the patio. The width of the patio is 12 feet. The length of the patio is two feet longer than the width.

How many feet of stone will Lorenzo need? Explain how you found your answer.

____ feet

Answer: 52 feet

Explanation:

Width = 12 feet

Length = 2 × width

Length = 2 + 12 feet = 14 feet

Perimeter = (2 × l) + (2 × w)

P = (2 × 14) + (2 × 12)

P = 28 + 24

P = 52 feet

### Page No. 754

Question 16.

Which rectangle has a perimeter of 10 feet? Mark all that apply.

Rectangle: ____

Rectangle: ____

Answer: A, C

Explanation:

i. Perimeter of A = (2 × l) + (2 × w)

P = (2 × 1) + (2 × 4) = 2 + 8 = 10 feet

ii. Perimeter of B = (2 × l) + (2 × w)

P = (2 × 2) + (2 × 5) = 4 + 10 = 14 feet

iii. Perimeter of C = (2 × l) + (2 × w)

P = (2 × 2) + (2 × 3) = 4 + 6 = 14 feet

iv. Perimeter of D = (2 × l) + (2 × w)

P = (2 × 4) + (2 × 6) = 8 + 12 = 20 feet

The correct answer is option A and C.

Question 17.

A folder is 11 inches long and 8 inches wide. Alyssa places a sticker that is 2 inches long and 1 inch wide on the notebook. Choose the words that correctly complete the sentence.

To find the number of square inches of the folder that is NOT covered by the sticker,

Type below:

________

Answer: Subtract the area of the sticker from the area of the notebook.

Question 18.

Tricia is cutting her initial from a piece of felt. For numbers 18a–18c, select Yes or No to tell whether you can add the products to find the number of square centimeters Tricia needs.

a. 1 × 8 and 5 × 2 _______

b. 3 × 5 and 1 × 8 _______

c. 2 × 5 and 1 × 3 and 1 × 3 _______

Answer:

a. 1 × 8 and 5 × 2 _______

Yes

b. 3 × 5 and 1 × 8 _______

No

c. 2 × 5 and 1 × 3 and 1 × 3 _______

No

Question 19.

Mr. Butler posts his students’ artwork on a bulletin board.

The width and length of the bulletin board are whole numbers. What could be the dimensions of the bulletin board Mr. Butler uses?

Type below:

________

Answer: 5 feet long by 3 feet wide

Area of the rectangle = l × w

A = 15 square feet

The factor of 15 is 5 and 3.

So, the length = 5 feet long

Width = 3 feet long.

Quick learning is not only important but also understanding is important to learn the concepts. You can’t love maths if you don’t understand the subject. So, to help you guys we have provided the images for your better understanding. Learn the simple techniques to solve the problem in less time in our Go Math Answer Key.

*Conclusion:*

Hope you are satisfied with the solutions provided in the Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area. For unlimited practice check out the questions in the review at the end of the chapter. You can also find all chapter’s solutions in our Go Math Answer Key. Make use of the links and score the highest marks in the exams. Best Of Luck!!!!