The area of a Square is defined as the space enclosed by the boundary of the square. Measurement of the area is done in square units. The unit for measurement of the area is m2.
The area of a square is found by multiplying the length of one side by itself.
Formula: Area of Square = (Side)2 unit2
Example: If a square has a side length of 4 cm, then its area is
Solution:
Given, side length (s) = 4 cm
Area of Square = s2 = 42 = 16 cm2Area of square with side length 4 cm is 16cm2
Area Using Diagonals
Area of Square when the diagonal length is given,
Area = (1/2) × d2
Where, d is Length of Diagonal.
Example: Find the Area of a square if the length of the diagonal is 6 cm.
Solution:
Given, diagonal length (d) = 6 cm
Area = (1/2) × d2
⇒ Area = (1/2) × 62
⇒ Area = 36/2 = 18cm2Area of square is 18cm2.
Using Perimeter
We can find an area if the perimeter of a square is given.
Formula of the perimeter of a square = 4 × side
From the above formula, we can find the side length by dividing the Perimeter by 4.
Side length(s) = Perimeter/4
Using side length, we can find the area of the square by using the formula: Area = side × side = (Perimeter/4)2.
Example: Find the Area of the Square if the perimeter of a square is 36 cm.
Solution:
Given, perimeter = 36 cm
So, Side length=perimeter/4
Side(s) = 36/4 = 9 cmFrom the side length we can calculate area of square by
Area = Side2 = 92 = 81 cm2
Area of square with perimeter 36 cm is 81 cm2.
Solved Examples
Example 1: Find the Area of the Square if the perimeter of a square is 64cm.
Solution:
Given, perimeter = 64cm
So, Side length = perimeter/4Side(s) = 64/4 = 16cm
From the side length we can calculate area of square by
Area =Side2
Area = 162 = 256 cm2Area of square with perimeter 64cm is 256cm2.
Example 2: Find the area of a square if the length of the diagonal is 12cm.
Solution:
Given, diagonal length (d) = 12 cm
Area = (1/2) × d2
Area = (1/2) × 122
Area = 144/2 = 72 cm2Area of square is 72 cm2.
Example 3: The length of each side of a square is 5 cm, and the cost of painting it is Rs. 5 per sq. cm. Find the total cost to paint the square.
Solution:
Given, Side length (s) = 5cm
Area of Square = s2
A = 52 = 25 cm2For 1 sq.cm cost of painting is Rs 5.
Total Cost of painting the 25sq cm= 25 × 5 = Rs125
Example 4: A floor that is 60 m long and 30 m wide is to be covered by square tiles of side 6 m. Find the number of tiles required to cover the floor.
Solution:
Length of the floor = 60 m
Breadth of the floor = 30 mArea of floor = length × breadth = 60 m × 30 m = 1800 sq. m
Length of one tile = 6 m
Area of one tile = side ×side = 6 m × 6 m = 36 sq. mNo. of tiles required = (area of floor)/(area of one tile) = 1800/36 = 50 tiles
Total tiles required is 50
Example 5: What is the Area of a Square if the perimeter of a square is 24 cm?
Solution:
Given, perimeter = 24 cm
So, Side length = perimeter/4
Side(s) = 24/4 = 6cmFrom the side length we can calculate area of square by
Area = Side2
Area = 62 = 36cm2Area of square with perimeter 24 is 36cm2.
