12.12 Circular compound shapes

A compound shape (also known as a composite shape) is one that is made from a number of smaller shapes. We have already looked at compound shapes made of triangles and quadrilaterals. Now we will look at compound shapes made of circles as well. 

Practice questions

Question 1

Finding the area of a compound shape

To calculate the area of a compound shape, we can use either of two methods:

• Addition method - Divide the compound shape into basic shapes, work out the area of each basic shape, then add them together.
• Subtraction method - Work out the area of the basic shape that encloses the compound shape, then subtract the areas of smaller basic shapes as necessary. 

We may also need to use a combination of the above methods. We can also try and re-arrange or visualise the shape in a different way.

How could we re-visualise the following shape up to make our calculations easier?

The shape consists of a square with side lengths of $10$10 cm and two semi circles

To find the area, we could work out the area of each semi circle individually, or we could join them back together to make one complete circle. This way we only need to work out the area of one square and one circle. Notice that if we calculated the semi-circular areas separately we are actually halving the area of the circle and then adding the two halves back together.

Similarly, to find the perimeter, by putting the two semi-circles back together we can work out the circumference of the full circle, and then add the two sides of the square that are on the outside of the shape. It is very important that you don't accidentally double-count sides.

Practice questions

Question 2