## AREA OF SQUARE

A square is a four-sided closed figure where the lengths of all the four sides will be equal and each vertex angle will be right angle or 90o as shown below. ## Formula for Area of a Square

Let s be the length of each side of a square.

Then, the formula for area of a square :

Area  =  s2

Let d be the length of each diagonal of a square.

Then, the formula for area of a square :

Area  =  1/2 ⋅ d2

## Examples

Example 1:

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

Solution:

When the length of a side is given, formula for area of a square :

=  s

Substitute 24 for s.

=  242

=  576

So, area of the square is 576 square cm.

Example 2:

If the area of a square is 64 square inches, then find the length of each side.

Solution:

Area of the square  =  64 in2

S2  =  64

Find positive square root on both sides.

√s2  =  √(8 ⋅ 8)

S  =  8

So, the length of each side of the square is 8 inches.

Example 3:

The square has side length 250 cm. Find its area in square meter.

Solution:

When the length of a side is given, formula for area of a square :

=  s

Substitute 250 for s.

=  2502

=  62500 cm2 -----(1)

We know

100 cm  =  1 m

Square both sides.

(100 cm)2  =  (1 m)2

1002 cm2  =  12 m2

10000 cm2  =  1 m2

Therefore, to convert centimeter square into meter square,  we have to divide by 10000.

(1)-----> Area of the square  =  62500 cm2

Divide the right side by 10000 to convert cm2 into m2.

Area of the square  =  (62500 / 10000) m2

6.25 m2

So, the area of the square is 6.25 square meter.

Example 4:

If the length of each diagonal is 2√2 cm, then find its area.

Solution:

When the length of a diagonal is given, formula for area of a square :

=  1/2 ⋅ d2

Substitute 2√2 for d.

=  1/2 ⋅ (2√2)2

Simplify.

=  1/2 ⋅ (4 ⋅ 2)

=  1/2 ⋅ (8)

=  4

So, the area of the square is 4 square cm.

Example 5:

If the lengths of the diagonals of two squares are in the ratio 2 : 5. then find the ratio of their areas.

Solution:

From the ratio 2 : 5, let the diagonals of two squares be 2x and 5x respectively.

When the length of a diagonal is given, formula for area of a square :

=  1/2 ⋅ d2

 Area of 1st square=  1/2 ⋅ (2x)2=  1/2 ⋅ (4x2)=  4x2 / 2 Area of 2nd square=  1/2 ⋅ (5x)2=  1/2 ⋅ (25x2)=  25x2 / 2

Ratio of the areas :

=  (4x2 / 2) : (25x2 / 2)

Multiply each term of the ratio by 2.

4x2 : 25x2

Divide each term by x2.

=  4 : 25

So, the ratio of the areas of two squares is 4 : 25. Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

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