Area of compound shapes
The area of a compound shape can be calculated by adding the areas of the shapes it is made from.
Example
Calculate the area of the compound shape.
Method 1
Calculate the area of the large rectangle.
\(8 \times (4 + 4 + 4) = 8 \times 12 = 96~\text{cm}^2\)
Calculate the area of the square which has been removed.
Subtract the area of this square from the rectangle.
\(96 - 16 = 80~\text{cm}^2\)
Method 2
Break the shape into two squares and a rectangle.
Calculate the area of each shape.
\(4 \times 4 = 16~\text{cm}^2\), \(4 \times 4 = 16~\text{cm}^2\), \(4 \times 12 = 48~\text{cm}^2\)
Add the three areas together.
\(16 + 16 + 48 = 80~\text{cm}^2\)