Area of a Square
Let us
find the formula to calculate the area of a square using the area of a
rectangle.
Consider a rectangle of length 5 cm
and breadth 3 cm. Draw this rectangle on a square grid sheet.
Count the number of squares that the rectangle covers. There are 15 squares. So, the area of a rectangle of sides 5 cm and 3 cm is 15 sq. cm.
Since 15 = 5 × 3, therefore the
product of the length and the breadth of the rectangle is equal to its area.
From this verified result, we can
conclude that
Area of a
rectangle = length × breadth
Let us consider the square now.
We know that a square is a rectangle
with all four sides equal.
We can use the same formula to find
the formula of area of a square.
Since, in a square, length = breadth
Area of a square = length × breadth =
length × length = side × side
Area of
a square = (side)2
Area of a Square Formula
Area of a Square Example
Example 1: Find the area of a square whose each side measures 15 cm.
Solution: Given: side of the square = 15 cm
Area of a square = (side)2
= (15)2
= 225 sq. cm
Example 2: The area of a square is 576 sq. cm. Find the measure of each side
of the square.
Solution: Given: area of the square = 576 sq. cm
We know that,
Area of a square = (side)2
576 = (side)2
(side)2 = 24 ×
24
side
= 24
Hence, the measure of each side of
square is 24 cm.
Example 3: Find
the cost of levelling a square field of side 25 m at the rate of Rs 20 per sq.
m.
Solution:
Given: The length of each side of the field = 25 m
The area of the square field = side ×
side
= 25 × 25 = 625 sq. m
The cost of levelling the field = 625 ×
20
= Rs 12,500
Example 4: Ritu
runs 1 km to complete one round of a square park. Find the area of
the park. Also, find the cost of
levelling the park at Rs 8 per sq. m.
Solution: Given:
The side of the square park = 1000/4 m = 250 m
The area of the park = (side)2 =
(250)2 = 62,500
m2
Cost of levelling the park = Rs 8
× 62,500 = Rs 5,00,000
Thus, the cost of levelling the park
at Rs 8 per sq. m is Rs 5,00,000.