## Area of Compound Shapes

A compound shape is a shape made up of different shapes.

Here is a compound shape:

To work out the area of this shape we can split it into two rectangles.

There are two ways of splitting the shape into two rectangles. We can split the shape like this:

To find the area of the whole shape we will work out the area of the two rectangles and add them together.

To find the area of a rectangle we need to multiply the length by the width.

We know the length and the width of the bigger rectangle. We need to find a missing length of the smaller rectangle.

The height of the whole shape is 9 cm and the height of the bottom shape is 5 cm. To find the height of the top shape we need to take 5 away from 9
9 - 5 = 4
(The smaller rectangle is a square)

We now have all the information we need to calculate the areas.

The area of the large rectangle is 5 × 10 = 50 cm2

The area of the square is 4 × 4 = 16 cm2

The area of the whole shape is 16 + 50
16 + 50 = 66 cm2

We could have also split the shape like this:

We need to find the base of the rectangle on the left. The base of the whole shape is 20 cm and the base of the shape on the right is 4 cm.
We need to calculate: 10 - 4

10 - 4 = 6 cm

The area of the rectangle on the left is 5 × 6 = 30 cm2

The area of the rectangle on the right is 4 × 9 = 36 cm2

The area of the whole shape is 30 + 36
30 + 36 = 66 cm2

Here is another compound shape:

To find the area of the compound shape we need to split it into a rectangle and a triangle.

We know the length and width of the rectangle.

The area of a triangle = 12 × base × height

We need to work out the base and the height of the triangle.

The base is 12 - 6 = 6 cm
The height is 11 - 4 = 7 cm

The area of the rectangle = 12 × 4 = 48 cm2

The area of the triangle = 12 × 6 × 7
12 × 6 × 7 = 3 × 7 = 21 cm2

The total area = 48 + 21 = 69 cm2

Try these:

Find the area of the shape:

Find the area of the shape:

In this shape we have a parallelogram cut out of a rectangle:

To find the area of this shape we need to take away the area of the parallelogram from the area of the rectangle.

The area of a rectangle = length × width

Area of rectangle = 11 × 7 = 77 cm2

The area of a parallelogram = base × height

Area of parallelogram = 2 × 5 = 10 cm2

The area of the shape = 77 - 10 = 67 cm2

In this shape we have a circle cut out of a triangle:

To find the area of this shape we need to take away the area of the circle from the area of the triangle.

The area of a triangle = 12 × base × height

The triangle's area = 12 × 9 × 11 = 992 = 49.5 cm2

The area of a circle = π × radius2

The radius of a circle is half of its diameter.
42 = 2 cm

The circle's area = π × 22
The circle's area = π × 4

We can write this as 4π cm2

We can leave our answer in terms of pi (if we have a calculator we can convert it to a decimal).

The area of the shape = 49.5 - 4π cm2

We can type this into a calculator to convert the answer to a decimal, this would give an answer of 36.9 cm2 to one decimal place.

Try this:

Find the area of the shape: