Area of a Rectangle

In the previous topic, by counting, we obtained an area of 15cm² for a 5cm by 3cm rectangle.

Notice also that 5 × 3 = 15

Thus, the area of a rectangle = “length or width” × “height”

Area =  w  ×  h 

Where  w  is the width
Where  h  is the height

If Area is given then to find h or w, we use the following formula:

Area   =  w    ×    h

width, w = \( \frac{Area}{h} \)

height, h = \( \frac{Area}{w} \)

Example 1:

Calculate the area of a rectangle of length 50cm and 30cm in width.

Solution:

Area   =  width  ×  height

= 30cm   ×     50cm

= 150cm²

Example 2:  

The area of a rectangle carpet is 20m². Find the length of the shorter side in metres if the length of the longer side is 4000mm.

Solution:

First, we have to convert 4000mm to m (millimetres to metres)

1000mm   =  1m

So 4000mm   = \( \frac{1}{1000} \: \times \: \scriptsize 4000 \\ = \frac{4000}{1000} \\ = \scriptsize 4m\)

If A   =   w   ×     h

height h = \( \frac{Area}{w} \\ = \frac{20m^2}{4m} \\ = \scriptsize 5m \)