## 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

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 :

= s2

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 = √64

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 :

= s2

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.

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