Area of Square

Concept Explanation

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 = $large side^2$ square units

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

Solution: Area of a square = $sidetimes side$

$=15times 15$

$=225 ;m^{2}$

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 = $sidetimes side$

$=18times 18$

$=324 ;m^{2}$

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 = $sidetimes side$

$=4.2times 4.2$

$=frac{42}{10}timesfrac{42}{10}$

$=frac{1764}{100}$

$=17.64;m^{2}$

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 = $sidetimes side$

$=15times 15$

$small =225 ;cm^{2}$

Also, the Side of square floor bathroom = 3 m

Hence, area of square floor bathroom = $sidetimes side$

$small =3times 3$

$small =9;m^{2}$

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.

Illustration: To find the side of a square when the area is 196 sq cm.

Solution: Let the side = y cm, Then Area = y X y

According to the question: Area= 196 sq cm

y X y = 196 sq cm OR $large y^2= 14^2$

y= 14 cm.

Hence the side of the square is 14 cm

Illustration: Find the area of a square of side length 1.55 m.

Solution: Area of a square = $large side^2$ = $(1.55)^{2}$ = 2.4025 $m^{2}$

Illustration: To find the side of a square when the area is 324 sq m.

Solution: Let the side = y m, Then Area = y X y

According to the question: Area= 324 sq m

y X y = 324 sq m OR $large y^2= 18^2$

y= 18 m.

Hence the side of the square is 18 m

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The ratio of the area of the square to that of the square drawn on its diagonal is ________________________.
A. 1 : 1	B. 1 : 2	C. 1 : 3	D. 1 : 4
Right Option : B
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Question : 2

What happens to area of a square if its side is doubled?
A. The area becomes 4 times the area of original square	B. The area becomes 1/4 times the area of original square	C. The area becomes 16 times the area of original square	D. The area becomes 1/16 times the area of original square
Right Option : A
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