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

**Area Word Problems Practice Questions**

**Practice**

**Problems**

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

**Solutions**

*Read and understand the question*. This question is looking for the area of a parallelogram when the base and height are given.*Read and understand the question*. This question is looking for the area of a triangle when the base and height are given.*Read and understand the question*. This question is looking for the base of a parallelogram when the area and height are given.*Read and understand the question*. This question is looking for the length of the side of a square backyard when the area is known.*Read and understand the question*. This question asks for the area of a circle when the radius is known.*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* = *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 cm^{2}.

*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.

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 m^{2}.

*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.

*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.

*Make a plan*. Use the formula *A* = *b* × *h* or *s*^{2}, and substitute the given value of the side.

*Carry out the plan*. Substitute the given values into the formula to get 144 =*s*^{2}. 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.

*Make a plan*. Use the formula *A* = π*r*^{2} and substitute the given value for the radius.

*Carry out the plan*. Substitute into the formula to get *A* = π × 7^{2} = 49π m^{2}.

*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.

*Make a plan*. Use the formula *A* = π*r*^{2} 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 × *r*^{2}. Divide each side of the equation by π to get *r*^{2} = 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 ft

^{2}

This answer is checking.

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