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.
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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.
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.
The length of the rectangle is $8m$ and the width is $5m$. Use the formula with these values.
$Area = l \times w \\Area = 8 \times 5$
$Area = \underline{40m^2}$