AREA OF SQUARE

About "Area of Square"

Area of Square :

In this section, we are going to learn, how to find area of a 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 90^o 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

Area of Square - 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 :

=  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  =  √(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 :

=  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

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. 

After having gone through the stuff given above, we hope that the students would have understood, "Area of Square". 

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