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Maths / Mensuration / Area of Square
(A Brief Glimpse of ABHYAS Content - Have aLook !!!!)

## Area of Square

A square is a quadrilateral in which it has 4 equal sides and all the interior angles of a square are right angles. It is a closed two-dimensional plane figure..

Area of a Square = Side × side = $\dpi{100} \large side^2$  square units

Illustration : Find the area of a square of side length 15 m.

Solution:  Area of a square = $side\times side$

$=15\times 15$

$=225 \;m^{2}$

Illustration: A square lawn has a side that is 18m long. Find the area of the lawn.

Solution: As side of the square lawn = 18 m

hence, area of the square lawn = $side\times side$

$=18\times 18$

$=324 \;m^{2}$

Illustration: A square park is to be watered. If one side of the park is 4.2 m, find the area to be watered?

Solution: Given: Side of the park = 4.2 m

Hence, area of square park to be watered = $side\times side$

$=4.2\times 4.2$

$=\frac{42}{10}\times\frac{42}{10}$

$=\frac{1764}{100}$

$=17.64\;m^{2}$

Illustration: A square tile is having the side of length 15 cm. How many such tiles would be required to cover the square floor of the bathroom of side 3 m?

Solution:  Length of the square tile = 15 cm

Hence, area of the square tile = $side\times side$

$=15\times 15$

$\small =225 \;cm^{2}$

Also, the Side of square floor bathroom = 3 m

Hence, area of square floor bathroom  = $side\times side$

$\small =3\times 3$

$\small =9\;m^{2}$

As area of square tile has units in cm but the units of area of square bathroom is in m.

Hence area of square bathroom in cm = 9 X 100 X 100

$\small =90,000\;cm^{2}$

Now, the number of tiles required  = $\small \frac{area \;of\; square\; floor\;}{Area \;of\;square\;tile}$

$\small =\frac{90000}{225}$

$\small =400$

Hence 400 tiles are required to cover the floor.

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