Area of squares and rectangles :
Area of squares and rectangles is the basic topic in mensuration.
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
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.
Example 1 :
Find the area of the square having side length 24 cm.
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.
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.
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) x (2x)²
= (1/2) x 4x² ==> 2x²
Area of second square = (1/2) x (5x)²
= (1/2) x 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.
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.
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
= 156 m
Cost of carpeting = 156 x 12.40 = $ 1934.40
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