2-dimensional shapes are flat. The perimeter of a 2D shape is the total distance around the outside of the shape. The area of a 2D shape is the space inside the shape.

Part of

The **area** of a 2D shape is the amount of space inside it. Examples of units of area are mm^{2}, cm^{2}, and m^{2}.

What is the area of this shape, if the area of each grid square is 1 cm^{2}?

There are 10 squares contained in this shape.

The area of the shape is 10 cm^{2}.

The area of each square is 1 cm^{2}. There are 12 squares contained in this rectangle.

The area of the rectangle is 12 cm^{2}.

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 = \(10 \times 5 = 50~\text{m}^2\)

The area of a compound shape can be calculated by adding the areas of the shapes it is made from.

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.

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