## AREA OF SQUARE

On this webpage area of square, we are gong to see how to find area of the given square.

## Ways to find area of square:

There are 3 ways to area of a square. We have to use one of the ways according to the information given in the question.

## Area when side length of square is given:

Area of the square = a²

Here "a" stands for the length of each side.

## How to find area of square if diagonal is given?

 Area of the square = d²/2here "d" stands for length of diagonal.

## How to find the area of a square when perimeter is given?

Side length of square   =   (1/4) x perimeter of square

Now let us see some example problems to understand this topic.

Example 1:

Find the area of the square having side length 24 cm.

Solution:

Area of the square = a² = 24²

= 24 x 24

= 576 cm²

Hence, area of square is 576 cm²

Example 2:

A square is of area 64 cm². Then find its side length.

Solution:

Area of the square = 64 cm²

a²  =  64 cm²

a  =  √64

=   √8 x 8 ==>  8 cm

Hence, side length of square is 8 cm

Example 3:

The square having side length 25 cm. Find the area in meter.

Solution:

Area of the square  = a²    =  25²  ==> 25 x 25 ==> 625 cm²

100 cm = 1 m

=  625/100  ==> 6.25 m²

Example 4:

Find the area of the square whose diagonal is measuring  4cm.

Solution:

The diagonal AC divides the square into two right triangles.Δ ACB and Δ ADC. In triangle ACB right angle is at B.

So the side which is opposite to right angle is called as hypotenuse.

By using Pythagorean theorem

AC²  =  AB² + BC²

4²  =  x² + x²

16  =  2x²

8  =  x²

√8  =  x

√2 x 2 x 2  =  x

2√2  =  x

Therefore, the length of each side is 2√2 cm

Area of the square  =  a²

=  (2√2)²

=  2²(√2)²

=  4 (2)

=  8 cm²

Example 5:

The diagonals of two squares are in the ratio 2:5. Find the ratio of their area.

Solution:

Let the diagonals of two squares be 2x and 5x respectively.

Area of a square when diagonal is given = (1/2) x d²

Area of first square  =  (1/2) (2x)²

=  (1/2)  4x²   ==> 2x²

Area of second square  =  (1/2) (5x)²

=  (1/2)  25x²   ==> 25x² / 2

Ratio of their areas ==> 2x²  :  (25x² / 2)

=   4 :  25

## More shapes

 Square Parallelogram Rectangle Rhombus Traingle Quadrilateral Area of quadrilateral Sector Hollow cylinder Sphere Area around circle Area around circle example problems Area of combined figures Example problems of area of combined figures Trapezium Area of trapezium Circle Semicircle Quadrant Example problems on quadrant Cyclinder Examples problems of cylinder Cone Hemisphere Example problems of hemisphere Path ways Area of path ways

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