Area of compound shapes

In a nutshell

Compound shapes are made out of two or more simple shapes. They can be broken up to find the total area these shapes cover.

Calculating the area

Compound shapes can be broken up into simpler shapes like rectangles or triangles. Then the areas of the individual simpler shapes can be calculated and added together for the total area. 

Example 1

What simple shapes can the compound shape below be broken up to?

There is a $$3$$​ sided shape with a right angle. 

There is a $$4$$ sided shape where the opposite sides are parallel. 

The compound shape can be broken up into a right angles triangle and a parallelogram.

Example 2

Find the area of the shape below. 

Break up the compound shape into two simpler shapes. 

The top right of the shape can represent a square. 

The bottom left of the shape can represent a rectangle. 

Calculate the area of each shape.

​$${Area\ of\ square} = 3 \times 3 = 9$$​​

​$${Area\ of\ rectangle} = 3 \times 2 = 6$$​​

Add the area of each shape for the area. 

​$$\underline{3+6 = 9 \ units^2}$$​​

Note: When you do not know the units you can write units squared.