A square has all its sides equal

Let lÂ =Â length of one side of a square.

Area = \( \scriptsize l \: \times \: l = l^2 \)

Area Â =Â \( \scriptsize l^2 \)

A = \( \scriptsize l^2 \)

If AreaÂ (A)Â 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:Â

A square room is 500cm long. Find the area in:Â **(a)** Square centimetres**(b)** Square metres

**Solution**

**(a)** Area of the room = l^{2}

= lÂ Ã—Â l

= 500cm Â Ã—Â Â 500cm

= 250 000 cm^{2}

**(b)** In Square meters:

1cm^{2} = \( \frac{1}{10000} \scriptsize \: or \: 0.0001 \: m^2\)

250 000 cm^{2} = \( \scriptsize 250,000 \: \times \: \normalsize \frac{1}{10000} \\ \scriptsize = 25m^2\)

### Example 2:

The area of a square hall is 225m^{2}. Find the length of one side of the square.

**Solution**

Area = l^{2}

The length of the square is 15m

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