Area of a Rectangle

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

Notice also that 5 × 3 = 15

Thus, the area of a rectangle = “Length” × “Width”

Area =  L  ×  W 

Where:

• L  is the Length
• W  is the width

If Area is given, then to find L or W, we use the following formula:

Area   =  L    ×    W

• Length, L = \( \frac{Area}{W} \)

• Width, W = \( \frac{Area}{L} \)

Example 8.2.1:

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

Solution:

Area   =  Length × Width

= 50 cm   ×     30 cm

= 150 cm²

Example 8.2.2:  

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

Solution:

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

1000 mm   =  1 m

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

If A   =   L   ×     W

W = \( \frac{Area}{L} \\ = \frac{20\: m^2}{4\:m} \\ = \frac{20\: m\: \times \: \not{m}}{4\:\not{m}}\\ = \scriptsize 5\:m \)