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Area of Complex Shapes Worksheet

Calculate the area of various complex shapes by decomposing them into simpler geometric figures.

Grade 9 Math GeometryArea of Complex Shapes
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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSG.GMD.A.3CCSS.MATH.CONTENT.HSG.GPE.B.7

Topics

mathgeometryareacomplex shapesgrade 9
8 sections · Free to use · Printable
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Area of Complex Shapes

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Read each question carefully and calculate the area of the complex shapes. Show all your work.

1. Find the area of the shape below. All angles are right angles. (Dimensions are in cm)

101044

2. Calculate the area of the composite figure shown. The top part is a semicircle. (Dimensions are in meters)

108

3. A complex shape is composed of a rectangle with dimensions 8 cm by 6 cm and a triangle with a base of 8 cm and a height of 5 cm. The total area of the complex shape is   cm².

4. Which of the following formulas represents the area of a shape made of a square with side 's' and an equilateral triangle with side 's' attached to one of its sides?

a

s² + (√3/4)s²

b

s² + (1/2)s²

c

2s + (√3/2)s

d

4s + 3s

5. To find the area of a complex shape, you must always divide it into rectangles and triangles only.

T

True

F

False

6. A rectangular garden is 15 ft long and 10 ft wide. A circular flower bed with a radius of 3 ft is in the center of the garden. Find the area of the garden NOT covered by the flower bed. (Use π ≈ 3.14)