Turns out, many things we see around us are actually made up of, or composed of, shapes such as triangles, rectangles, squares and parallelograms. This means they are composite shapes, so to work out their area we can use what we know about finding:

the area of rectangles (including squares)
the area of triangles, and
the area of parallelograms.

Two different methods

To work out the area of a composite shape, you can use either of two methods, and this is true of any composite shape. You can:

work out the area of a shape that includes, but is bigger than, your composite shape, and subtract section(s), or
work out the area of the smaller shapes that make up the composite shape.

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

How can I work out the area of THAT?

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. Could you imagine it would be possible, at the start?

Created with Geogebra

Worked Examples

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.

Determine the area of rectangle $B$B.
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.

Remember!

You can choose which method to use to work out the area of composite shapes, and there can even be more than one way to make up a composite shape.

Area of Composite Shapes

Which shape is that?