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?

L shape measuring 4x2x2x1x2x3 squares

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.

3x4cm rectangle. The smaller squares that make up the rectangle, are labelled 1-12

The area of the rectangle is 12 cm2.

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

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

Area = length (l) x width (w)
Question

What is the total area of the field?

Two sides labelled 5 & 10 cm

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.

Side dimensions of the U shape

Method 1

Calculate the area of the large rectangle.

Area of the compound shape with side dimensions labelled

\[8 \times (4 + 4 + 4) = 8 \times 12 = 96~\text{cm}^2\]

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.

Calculating the area of the compund shape using it's constituent shapes

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.

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