Area Word Problems Practice Questions

To review these concepts, go to Area World Problems Study Guide.

Area Word Problems Practice Questions

Practice

Problems

1. What is the area of a rectangle with a base of 6 cm and a height of 5 cm?
2. The base of a triangle is 12 m and the height is 14 m. What is the area of the triangle?
3. The area of a parallelogram is 52 cm²and the height is 13 cm. What is the base of the parallelogram?
4. A square backyard has an area of 144 square feet. What is the length of a side of the backyard?
5. A circle has a radius of 7 m. What is the area of the circle?
6. The area of a circular animal pen is 196π square feet. What is the diameter of the pen?

Solutions

1. Read and understand the question. This question is looking for the area of a parallelogram when the base and height are given.

Make a plan. Use the formula A = b × h and substitute the given values to find the area.

Carry out the plan. Substitute the given values into the formula to get A = 6 × 5 = 30 cm².

Check your answer. To check the solution, divide the area by one of the dimensions and make sure the result is the other dimension: 30 ÷ 6 = 5.

This answer is checking.

2. Read and understand the question. This question is looking for the area of a triangle when the base and height are given.

Make a plan. Use the formula A=bh and substitute the given values to find the area.

Carry out the plan. Substitute the given values into the formula to get (12)(14) = (168) = 84 m².

Check your answer. To check the solution, work backward by doubling the area and then dividing this result by one of the dimensions to make sure the result is the other dimension.

2 × 84 = 168
168 ÷ 12 = 14

This answer is checking.

3. Read and understand the question. This question is looking for the base of a parallelogram when the area and height are given.

Make a plan. Use the formula A = b × h and substitute the given values to solve for the base.

Carry out the plan. Substitute the given values into the formula to get 52 = b × 13. Divide each side of the equation by 13 to get b = 4 cm.

Check your answer. To check the solution, divide the area by one of the dimensions, and make sure the result is the other dimension: 52 ÷ 4 = 13. This answer is checking.

4. Read and understand the question. This question is looking for the length of the side of a square backyard when the area is known.

Make a plan. Use the formula A = b × h or s², and substitute the given value of the side.

Carry out the plan. Substitute the given values into the formula to get 144 =s². Take the positive square root of each side of the equation to get s = 12 ft.

Check your answer. To check the solution, square the length of a side and make sure the result is the area: 12 × 12 = 144. This answer is checking.

5. Read and understand the question. This question asks for the area of a circle when the radius is known.

Make a plan. Use the formula A = πr² and substitute the given value for the radius.

Carry out the plan. Substitute into the formula to get A = π × 7² = 49π m².

Check your answer. To check the solution, divide the area by π times the radius. The result is 7, which is the length of the radius. This answer is checking.

6. Read and understand the question. This question asks for the diameter of a circle when the area is known.

Make a plan. Use the formula A = πr² and substitute the given value for the area. Then, solve the equation for r and multiply the result by 2 to find the diameter.

Carry out the plan. Substitute into the formula to get 196π = π × r². Divide each side of the equation by π to get r² = 196. Take the positive square root of each side of the equation to get r = 14. Multiply this result by 2 to find the length of the diameter: 2 × 14 = 28 ft.

Check your answer. To check the solution, divide the diameter by 2 and substitute this value into the area formula.

28 ÷ 2 = 14
A = π(14)² = 196π ft²

This answer is checking.