Area of rectilinear shapes

In a nutshell

The area of a shape is the amount of space inside the shape. The area of a square or rectangle can be found by either counting the number of $1cm^2$ inside the shape, or using formulae for the area of a square or the area of a rectangle.

Finding the area using squares

The area of a rectilinear figure can be worked out by counting the squares inside a shape. If each square counted is $1cm^2$ , the total area is the number of squares multiplied by $1cm^2$ .

Example 1

Find the area of the rectangle by counting squares.

Maths; Measurement; KS2 Year 4; Area of rectilinear shapes

First count the number of squares in the rectangle.

The total number of squares is $14$ .

Find the total area of the shape if each square is $1cm^2$ .

The total area of the rectangle is $\underline{14cm^2}$ .

Finding the area of a square using a formula

If you have the length of a side in a square, it is possible to work out the area using the formula for the area of a square. The formula for the area of a square is given by:

A=x^2

$A$	The Area of the square.
$x$	The length of a side.

Example 2

Find the area of the square.

Maths; Measurement; KS2 Year 4; Area of rectilinear shapes

The square is shown on a centimetre square grid, so each side has length $4cm$ . The area is given by

$\begin {aligned}Area &=x^2 \\Area &=4^2 = 4 \times 4 \\ Area &= \underline{16cm^2}\\\end {aligned}\\$ 

Finding the area of a rectangle using a formula

If you have the length and width of a rectangle, it is possible to work out the area using the formula for the area of a rectangle. The formula for the area of a rectangle is given by:

A=l \times w

$A$	The Area of the rectangle.
$l$	The length of the rectangle.
$w$	The width of the rectangle.

Example 3

Find the area of the rectangle.

	$8m$
$5m$

The length of the rectangle is $8m$ and the width is $5m$ . Use the formula with these values.

$Area = l \times w \\Area = 8 \times 5$ 

$Area = \underline{40m^2}$