FINDING AREA OF COMPOSITE FIGURES WORKSHEET

Work out the shaded area.

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Shown is a triangular brick wall with a rectangular window. Find the area of the wall that is brick.

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Find the area of the garden that is grass.

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Find the area of the composite shapes given below.

Problem 6 :

You are deciding on two different designs for envelopes.

a. Which design has the greater area?

b. You make 500 envelopes using the design with the greater area. Using the same amount of paper, how many more envelopes can you make with the other design?

Problem 7 :

Find the area of the figure

Find the area of the figure.

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Problem 11 :

The diagram shows the plan of a field. The farmer sells the field for £3 per square metre. Work out the total amount of money the farmer should get.

Problem 12 :

The diagram shows a rectangle inside a triangle. The triangle has a base of 12 cm and a height of 10 cm. The rectangle is 5 cm by 3 cm. Work out the area of the region shown shaded in the diagram.

Problem 13 :

You use the parallelogram-shaped sponge to create the T-shirt design. The area of the design is 66 square inches. How many times do you use the sponge to create the design? Draw a diagram to support your answer.

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Problem 10 :

You make a photo prop for a school fair. You cut a 10-inch square out of a parallelogram-shaped piece of wood. What is the area of the photo prop? 

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Problem 11 :

You can use a trapezoid to approximate the shape of Scott County, Virginia. The population is about 23,200. About how many people are there per square mile?

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Problem 12 :

Light shines through a window. What is the area of the trapezoid-shaped region created by the light?

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Problem 13 :

The triangle and the trapezoid share a 15-inch base and a height of 10 inches.

a. The area of the trapezoid is less than twice the area of the triangle. Find the values of x. Explain your reasoning.

b. Can the area of the trapezoid be exactly twice the area of the triangle? Explain your reasoning.

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Find the area of compound shapes given below.

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Problem 7 :

Your family hires a company to install invisible fencing around your yard.

Part A : Find the area of the yard using only the area formulas for rectangles and triangles. Show your work.

Part B : Find the area of the yard using the area formula for trapezoids.

Part C : Explain why the two methods of finding the area of the yard give the same result. Describe the advantages of each method.

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Problem 8 :

The figure is made up of a square and a rectangle. Find the area of the shaded region.

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Problem 9 :

The fountain is made up of two semicircles and a quarter circle. Find the perimeter and area of the fountain.

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Find the area of the shaded region.

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Answer Key

1)  205 cm²

2)   area of the shape is 3640 cm²

3)  125.5 cm²

4)  25.87 cm²

5)  365.97 cm²

6)  139.36 cm²

7)  a)   435 square feet    b)  435 square feet

c)  The easiest way is using the formula of trapezoid, because using one formula we will find the area of the shape.

8)  22.5 square meter

9)   235.5 square meter.

10)  89 square meter

11)   23.5 square inches

12)  21.87 square feet