# Area of squares, rectangles and compound shapes

The area of a 2D shape is the amount of space inside it. Examples of units of area are mm2, cm2, and m2.

### Example

What is the area of this shape, if the area of each grid square is 1 cm2?

There are 10 squares contained in this shape.

The area of the shape is 10 cm2.

## Area of squares and rectangles

The area of each square is 1 cm2. There are 12 squares contained in this rectangle.

The area of the rectangle is 12 cm2.

The area of a rectangle can also be calculated using the following formula.

$\text{Area of a rectangle} = \text{length} \times \text{width}$

Question

What is the total area of the field?

Area = $$10 \times 5 = 50~\text{m}^2$$

## 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.

$16 + 16 + 48 = 80~\text{cm}^2$