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McGraw-Hill Math Grade 7 Answer Key Lesson 19.4 Metric Perimeter, Area, and Volume of a Solid
Exercises
CALCULATE
Question 1.
What is the perimeter of a square with sides of 7 cm?
What is the area?
Answer:
Perimeter of the square = 28 cm.
Area of the square = 49 square cm.
Explanation:
Side of the square = 7 cm.
Perimeter of the square = 4 × Side of the square
= 4 × 7
= 28 cm.
Area of the square = Side of the square × Side of the square
= 7 × 7
= 49 square cm.
Question 2.
The perimeter of this figure with 6 equal sides is 48 millimeters. What is the length of each side?
Answer:
Length of the each side = 8 mm.
Explanation:
Number of sides of the figure = 6.
Perimeter of this figure = 48 millimeters.
Length of the each side = Perimeter of this figure ÷ Number of sides of the figure
= 48 ÷ 6
= 8 mm.
Question 3.
A cube has sides of 6 cm. What is the volume of the cube?
What is the surface area of the whole figure?
Answer:
Volume of the cube = 216 cubic cm.
Surface area of the cube = 36 square cm.
Explanation:
Side of the cube = 6 cm.
Volume of the cube = Side of the cube × Side of the cube × Side of the cube
= 6 × 6 × 6
= 36 × 6
= 216 cubic cm.
Surface area of the cube = 6 × Side of the cube
= 6 × 6
= 36 square cm.
Question 4.
A rectangle has sides of 2.4 cm and 8 cm. What is the perimeter of the rectangle?
What is the area of the rectangle?
Answer:
Perimeter of the rectangle = 20.8 cm.
Area of the rectangle = 19.2 square cm.
Explanation:
Length of the rectangle = 8 cm.
Width of the rectangle = 2.4 cm.
Perimeter of the rectangle = 2(Length of the rectangle + Width of the rectangle)
= 2(8 + 2.4)
= 2 × 10.4
= 20.8 cm.
Area of the rectangle = Length of the rectangle × Width of the rectangle
= 8 × 2.4
= 19.2 square cm.
Question 5.
What is the perimeter of this rectangle with sides of 14 meters and 6 meters?
What is the area?
Answer:
Perimeter of the rectangle = 40 m.
Area of the rectangle = 84 square m.
Explanation:
Length of the rectangle = 14 m.
Width of the rectangle = 6 m.
Perimeter of the rectangle = 2(Length of the rectangle + Width of the rectangle0
= 2(14 + 6)
= 2 × 20
= 40 m.
Area of the rectangle = Length of the rectangle × Width of the rectangle
= 14 × 6
= 84 square m.
Question 6.
Damian designed a course around his neighborhood to race his bicycle with friends. His neighborhood is in the shape of a regular pentagon with 5 equal sides measuring 500 meters each. If Damian can ride his bicycle at a speed of 20 km per hour, how many times around the course will he go in an hour?
Answer:
Number of times around the course will he go in an hour = 125.
Explanation:
Number of sides His neighborhood is in the shape of a regular pentagon = 5.
Length of the each side = 500 m.
Perimeter of the pentagon = Number of sides His neighborhood is in the shape of a regular pentagon × Length of the each side
= 5 × 500
= 2,500 m.
Speed of Damian can ride his bicycle = 20 km per hour.
Number of times around the course will he go in an hour = Perimeter of the pentagon ÷ Speed of Damian can ride his bicycle
= 2,500 ÷ 20
= 125.
Question 7.
Anabelle is buying a new rug for her living room. The rug store prices the rug by the square meter. If Anabelle needs a rug with dimensions of 3.7 meters long and 2 meters wide, and the rug store charges $12.00 per square meter, how much will she pay for a new rug? ______________
What is the perimeter of the rug? ______________
Answer:
Amount of money she needs to pay for new rug = $88.8.
Perimeter of the rug = 11.4 m.
Explanation:
Length of the rug = 3.7 m.
Width of the rug = 2 m.
Area of the rug = Length of the rug × Width of the rug
= 3.7 × 2
= 7.4 square m.
Amount of money rug store chargers for the rug = $12.00 per square meter.
Amount of money she needs to pay for new rug = Area of the rug × Amount of money rug store chargers for the rug
= 7.4 × 12
= $88.8.
Perimeter of the rug = 2(Length of the rug + Width of the rug)
= 2(3.7 + 2)
= 2 × 5.7
= 11.4 m.
Question 8.
What is the volume of the rectangular solid?
Answer:
Volume of the rectangular solid = 900 cubic cm.
Explanation:
Length of the rectangular solid = 18 cm.
Width of the rectangular solid = 10 cm.
Height of the rectangular solid = 5 cm.
Volume of the rectangular solid = Length of the rectangular solid × Width of the rectangular solid × Height of the rectangular solid
= 18 × 10 × 5
= 180 × 5
= 900 cubic cm.
Question 9.
What is the area of the triangle?
Answer:
Area of the triangle = 35 square m.
Explanation:
Base of the triangle = 14 m.
Height of the triangle = 5 m.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 14 × 5
= \(\frac{1}{1}\) × 7 × 5
= 35 square m.
Question 10.
How much water can a swimming pool with a flat bottom hold? It is 12 meters long, 8 meters wide, and 2.5 meters deep.
Answer:
Number of liters of water can a swimming pool with a flat bottom hold = 2,40,000 liters.
Explanation:
Length of the swimming pool = 12 m.
Width of the swimming pool = 8 m.
Height of the swimming pool = 2.5 m.
Volume of the swimming pool = Length of the swimming pool × Width of the swimming pool × Height of the swimming pool
= 12 × 8 × 2.5
= 96 × 2.5
= 240 cubic m.
Number of liters of water can a swimming pool with a flat bottom hold =
Conversion:
1 cubic m= 1,000 liters.
240 cubic m = ?? liters
=> 1 × ?? = 1,000 × 240
=> ?? = 2,40,000 liters.
Question 11.
What is the area of the triangle?
Answer:
Area of the triangle = 96 square m.
Explanation:
Base of the triangle = 12 m.
Height of the triangle = 16 m.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 12 × 16
= \(\frac{1}{1}\) × 6 × 16
= 96 square m.
Question 12.
What is the area of this rectangle?
Answer:
Area of the rectangle = 192 square mm.
Explanation:
Length of the rectangle = 16mm.
Width of the rectangle =Â 12mm.
Area of the rectangle = Length of the rectangle × Width of the rectangle
= 16 × 12
= 192 square mm.