# AREA OF SQUARES AND RECTANGLES

## About "Area of Squares and Rectangles"

Area of squares and rectangles :

Area of squares and rectangles is the basic topic in mensuration.

 Square :A plane figure with four equal straight sides and four right angles is called square.

Area of square :

Generally there are 3 ways to find area of a square. We have to use one of those ways according to the information given in the question.

Area of the square = a²

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

Area of the square = d²/2

here "d" stands for length of diagonal.

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

 Rectangle :A plane figure with four straight sides and four right angles.In which the opposite sides are having the same length.

Area of rectangles :

Area of rectangle  =  L x W

Here "L" represents length of the rectangle and "W" represents the width of the rectangle.

## Area of square and rectangles - Example problems

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 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

Example 4 :

The length and width of the rectangle are in the ratio 5:2 .If the area of the rectangle is measuring 147 cm². Then find the length and width of the rectangle.

Solution :

5x and 2x be the length and width of the rectangle respectively.

Area of the rectangle = 147 cm²

Length x width  =  147

5x x 2x  =  147

7x²  =  147

x²  =  147/7

x²  =  21

x  =  √21

Length  =  5x  =  5√21 cm

Width  =  2x  =  2√21 cm

Example 5 :

Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of \$12.40 per square meter.

Solution :

From the given information we come to know that

Area of carpet  =  Area of room  ---- (1)

area of rectangle  =  length  x width

0.75 x width of carpet  =  13 x 9

width of carpet  =  (13 x 9) /0.75

=  117/0.75

=  156 m

Cost of carpeting = 156 x 12.40 = \$ 1934.40

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