Example A

Find the area of the following shape:

15 cm

12 cm

7 cm

6 cm

This shape can be divided into a rectangle and a triangle in a number of ways. This is one way:

15 cm

12 cm

7 cm

6 cm

This shape can be divided into a rectangle and a triangle in a number of ways. This is one way:

15 cm

12 cm

7 cm

6 cm

This shape can be divided into a rectangle and a triangle in a number of ways. This is one way:

15 cm

12 cm

7 cm

6 cmRectangle

This shape can be divided into a rectangle and a triangle in a number of ways. This is one way:

15 cm

12 cm

7 cm

6 cmRectangle

Triangle

So we have a Rectangle that measures 7 cm × 12 cm.

12 cm

7 cm

Rectangle

So we have a Rectangle that measures 7 cm × 12 cm.

12 cm

7 cm

Rectangle

So the area is 7 × 12 =

So we have a Rectangle that measures 7 cm × 12 cm.

12 cm

7 cm

Rectangle

So the area is 7 × 12 = 84 cm2.

We can work out the base of the triangle by subtracting 7 cm from 15 cm.

15 cm

7 cm

Triangle

Base

We can work out the base of the triangle by subtracting 7 cm from 15 cm.

15 cm

7 cm

Triangle

Base

So this is 8 cm.

And we can work out the height by subtracting 6 cm from 12 cm. So this is 6 cm.

12 cm

6 cm

HeightTriangle

And we can work out the height by subtracting 6 cm from 12 cm. So this is 6 cm.

12 cm

6 cm

HeightTriangle

So this is 6 cm.

And we can work out the height by subtracting 6 cm from 12 cm. So this is 6 cm.

12 cm

6 cm

HeightTriangle

So this is 6 cm.

So the area of the triangle is ½ × 8 × 6 = 24 cm2.

Adding the two gives a total area of

84cm2

24cm2

84 + 24 =

Adding the two gives a total area of

84cm2

24cm2

84 + 24 = 108 cm2.