Geometry: Area and Perimeter (Middle School) Worksheet

Question 1

A rectangle is 12 centimeters long and 7 centimeters wide. Find its area and perimeter.

Accepted Answer

The area is 84 square centimeters because 12 × 7 = 84. The perimeter is 38 centimeters because 2(12 + 7) = 38.

Question 2

A square garden has a side length of 9 feet. Find the area and perimeter of the garden.

Accepted Answer

The area is 81 square feet because 9 × 9 = 81. The perimeter is 36 feet because 4 × 9 = 36.

Question 3

A triangle has a base of 14 inches and a height of 6 inches. Find the area of the triangle.

Accepted Answer

The area is 42 square inches because the area of a triangle is 1/2 × base × height, so 1/2 × 14 × 6 = 42.

Question 4

A parallelogram has a base of 10 meters and a height of 8 meters. Find its area.

Accepted Answer

The area is 80 square meters because the area of a parallelogram is base × height, so 10 × 8 = 80.

Question 5

A trapezoid has bases of 16 centimeters and 10 centimeters. Its height is 5 centimeters. Find the area.

Accepted Answer

The area is 65 square centimeters because A = 1/2(b1 + b2)h, so 1/2(16 + 10)5 = 65.

Question 6

A rectangular classroom floor is 24 feet long and 18 feet wide. Carpet costs $3 per square foot. How much will it cost to carpet the whole floor?

Accepted Answer

The floor area is 432 square feet because 24 × 18 = 432. The carpet will cost $1,296 because 432 × 3 = 1,296.

Question 7

A rectangular picture frame measures 20 inches by 15 inches. What is the perimeter of the frame?

Accepted Answer

The perimeter is 70 inches because 2(20 + 15) = 70.

Question 8

Find the area of an L-shaped figure made from two rectangles. The first rectangle is 8 feet by 4 feet. The second rectangle is 3 feet by 6 feet. The rectangles do not overlap.

Accepted Answer

The total area is 50 square feet because the first rectangle has area 8 × 4 = 32 and the second rectangle has area 3 × 6 = 18, and 32 + 18 = 50.

Question 9

A rectangle has an area of 96 square centimeters and a width of 8 centimeters. What is its length?

Accepted Answer

The length is 12 centimeters because area = length × width, and 96 ÷ 8 = 12.

Question 10

A square has a perimeter of 52 meters. What is the length of one side, and what is the area of the square?

Accepted Answer

One side is 13 meters because 52 ÷ 4 = 13. The area is 169 square meters because 13 × 13 = 169.

Question 11

A triangular flag has side lengths of 9 inches, 12 inches, and 15 inches. What is the perimeter of the flag?

Accepted Answer

The perimeter is 36 inches because 9 + 12 + 15 = 36.

Question 12

A park is shaped like a rectangle with a length of 60 yards and a width of 35 yards. A fence will be placed around the park. How many yards of fencing are needed?

Accepted Answer

The park needs 190 yards of fencing because the perimeter is 2(60 + 35) = 190.

Question 13

A composite shape is made by placing a rectangle and a triangle together. The rectangle is 10 inches long and 6 inches wide. The triangle has a base of 10 inches and a height of 4 inches. Find the total area.

Accepted Answer

The rectangle area is 60 square inches because 10 × 6 = 60. The triangle area is 20 square inches because 1/2 × 10 × 4 = 20. The total area is 80 square inches.

Question 14

A regular hexagon has side lengths of 7 centimeters. What is its perimeter?

Accepted Answer

The perimeter is 42 centimeters because a hexagon has 6 sides and 6 × 7 = 42.

Question 15

A student says that a rectangle with an area of 48 square units must have a perimeter of 28 units. Give one example that proves the student is not always correct.

Accepted Answer

One example is a rectangle with side lengths 6 units and 8 units. Its area is 48 square units, but its perimeter is 28 units. To prove the statement is not always correct, another example is 4 units by 12 units, which also has area 48 square units but has perimeter 32 units.

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Geometry: Area and Perimeter (Middle School)

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