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

If the length of the diagonal of a square and that of the side of another square are both 10 cm, the ratio of the area of first square to that of the second is ________________-

Right Option : A
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Explanation
Question : 2

Find the area of square plot of side 8 m.

Right Option : B
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Explanation
Question : 3

A square whose diagonal is 10 cm long has area equal to ___________________.

 

Right Option : C
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Explanation
 
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