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4. Measurement
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AustraliaWA
Year 11

4.045 Composite areas

Lesson
Worksheet
Practice
Lesson

Area of composite shapes

A composite shape is a shape that is made up of two or more other shapes such as triangles, rectangles and squares. 

Two methods to calculate area of a composite shape:
  • calculate the area of a shape that includes, but is bigger than, your composite shape, and subtract section(s),
    or
  • calculate the area of the smaller shapes that make up the composite shape and add the sections together.

Let's see how to do it, using a roof section, and working it out both ways. 

In this applet, you'll see an unusual shape. By revealing the shapes, one by one, you can see how the area could be calculated. 

Created with Geogebra

 

Practice questions

QUESTION 1

Consider the given shape.

The composite figure consists of two rectangles, labeled A and B. Rectangle A is placed on top of Rectangle B. Rectangle A is longer than Rectangle B. The length of rectangle A measures 9 cm.  The width of rectangle A measures 1 cm. The width of rectangle B measures 5 cm.  Rectangle A extends 4 cm beyond Rectangle B on the left side. Rectangle A extends 2 cm beyond Rectangle B on the right side. The length of rectangle B, 3 cm, is not explicitly labeled.

  1. Determine the area of rectangle $B$B.

  2. Hence calculate the total area of the composite shape.

QUESTION 2

Find the shaded area in the figure shown.

QUESTION 3

Find the total area of the figure shown.

Outcomes

1.3.8

calculate areas of rectangles and triangles, and composites of these shapes

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