The area of a rectangle is the amount of space taken up by the rectangle. To find the area of a rectangle, we simply have to multiply its length by its width. Hence, the formula to find the area of a rectangle is:
$$\LARGE{A = lw}$$
where \({l}\) is the length and \({w}\) is the width
Let's apply this formula by taking a look at a few examples.
Example 1: What is the area of the rectangle below?
Here we have a rectangle that is 19 feet long and 13 feet wide. Therefore, our length is 19 ft and width is 13 ft.
Remember that the area of a rectangle is the length times the width. Applying the formula, we get
$$\eqalign{
A & = lw \cr
& = \left( {19} \right)\left( {13} \right) \cr
& = 247 \cr} $$
Don't forget, we always write the area as units squared. So, the area of the rectangle above is 247 feet squared or 247 ft2.
Example 2: The area of a rectangular yard is 120 m2. If the width is 8 meters, find the length.
Since we know the area, \(A=120\), and the width, \(w=8\), this makes it easy for us to find the length using the formula
$$\eqalign{
A& = lw \cr
120 &= \left( l \right)\left( 8 \right) \cr
120 &= 8l \cr
{{120} \over 8} &= {{8l} \over 8} \cr
15& = l \cr} $$
Therefore, the length of the rectangular yard is 15 meters.