What is an Area?

The area or space occupied by any object or is a region occupied by any shape is called an area. In a square, all four sides are equal in size, which means the area of a square is equal to the side square.

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Area of Square 

The area of the square is defined as the region covered by all four sides of the square in a 2D plane, mathematically 

The area of a square is = side²

Algebraically the area of a square can find by the squaring of the sides let's see for an example-

Ques- A square having a side = 8cm. Find the area of a square?

Ans-  we know the side of the square = 8cm 

        = 8x 8

        =64cm²

  The area of the square is =64cm²

 Perimeter of Square

The perimeter of a square is defined as the total measurement of the length of four sides. We know that a square has four sides therefore the perimeter of the square will be 4a

 Perimeter of Square = 4a

Where,

       a is the side of any square

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 How to find the area of a Square using a Diagonals

The area of a square also can be calculated by using the diagonals of the square let's see how?

Suppose a square of side (s) having diagonal (d) now you can put the Pythagoras theorem –

     d² = s² + s²

     d² = 2s²

     d = √2 s 

     s  =  d/√2

Now this formula help in finding the area of square 

Now we know the area of square = s² = (d/√2)² 

                                                            = d²/2

 Solved Questions

Que 1- Find the area of a square of side = 9cm?

Ans- we know the area of square = side²

         =9 x 9

         = 81cm²

Que 2- Find the area of square white board having perimeter = 48 cm

Ans- we known that perimeter of square = 4a

              48=4a

              a=48/4 =12cm

Area of square=side²

             = 12² =144cm²

Que 3- Find the area of park having diagonal = 6cm ?

Ans- We known that area of square when diagonal is given= d²/2

              =6²/2

              =36/2 =18cm²

Que 4- Find the length of green board having area 81cm² ?

Ans- Area of square = side² 

            side² = 81 

            Side = √81

                   =  9cm