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Lesson 8, Topic 3
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Area of a Square

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A square has all its sides equal

Let l  =  length of one side of a square.

Area  = $$\scriptsize l \: \times \: l = l^2$$

Area  =  $$\scriptsize l^2$$

A = $$\scriptsize l^2$$

If Area  (A)  is given, then l can be found by taking the square root of both sides.

$$\scriptsize \sqrt{l^2} = \sqrt{A}$$

$$\scriptsize \therefore \: l = \sqrt{A}$$

Example 1:

A square room is 500cm long. Find the area in:

(a) Square centimetres
(b) Square metres

Solution

(a) Area of the room = l2

= l  ×  l

= 500cm   ×   500cm

= 250 000 cm2

(b) In Square meters:

1cm2 = $$\frac{1}{10000} \scriptsize \: or \: 0.0001 \: m^2$$

250 000 cm2 = $$\scriptsize 250,000 \: \times \: \normalsize \frac{1}{10000} \\ \scriptsize = 25m^2$$

Example 2:

The area of a square hall is 225m2. Find the length of one side of the square.

Solution

Area = l2

$$\scriptsize l = \sqrt{A}$$

$$\scriptsize l = \sqrt{225}$$

$$\scriptsize l = 15m$$

The length of the square is 15m