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 $$1cm^2$$.

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Example 1

Find the area of the rectangle by counting squares.

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:

Example 2

Find the area of the square.

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

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

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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:

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.

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

​$$Area = \underline{40m^2}$$​​