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.
Let's understand the Area of square with the following illustration:
To calculate square's area we need to know the length of any of its sides. The area of the square can be calculated by squaring the length of any of its sides.
For example, if side of a square is 6 cm, then the area is 6 x 6 = 36 cm2
If side of a square is 9 km, then the area is 9 x 9 = 81 km2
What is a Square?
Square is a type of quadrilateral (polygon with four sides) with with four equal sides and angles and all the angles measure 90 degree.
Some common properties of squares are:
- All four sides of a square are of equal length.
- Each internal angle of a square measures 90 degrees.
- Diagonals of a square intersect each other at right angles and bisect each other, dividing the square into four congruent right-angled triangles.
- Diagonals of a square are equal in length.
- A square has rotational symmetry of order four, meaning it looks the same after a rotation of 90°, 180°, or 270°.
There are various formulas for finding the area of the square but the most basic one is the Area the of Square using Side Length the formula for which is added below:
Area of Square = (Side)2 unit2
The image added below shows a square of side (s) and then its area is (s2).
Area can be measured in various units, some of the conversions for changing standard units of the area to other desired units are given below:
- 1 m2 = 10000 cm2
- 1 km2 = 1000000 m2
If required in calculation we can find the perimeter of the square by the given formula.
Perimeter of Square = 4 × sides units
Let's consider an example to understand the use of the formula for the area of the square.
Example: What is the Area of a square if each side of the length is 4cm?
Solution:
Given, side length (s) = 4 cm
Area of Square = s2 = 42 = 16 cm2
Area of square with side length 4 cm is 16cm2
How to Find Area of Square?
Area of the square can be calculated if the dimensions of the square are known. We can calculate the area of the square by various formulas depending on the initial values that are given.
Follow the steps given below to find the area of the square.
Step 1: Note the dimension of the square given. For example to find the area of a square with a side of 10 m. The given dimension (side) is 10 m.
Step 2: Use the area of the Square formula. As Area of Square = (Side)2. For given example,
Step 3: Simplify the value obtained in step 2. For given example,
- Area of Square = (10)2 = 100
Step 4: Add unit2 as the unit to the answer obtained in step 3 to get the final answer. For given example,
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 6cm.
Solution:
Given, diagonal length (d) = 6 cm
Area = (1/2) × d2
⇒ Area = (1/2) × 62
⇒ Area = 36/2 = 18cm2
Area 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 cm
From 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.
Related Articles:
Solved Examples on Area of Square
Example 1: Find the Area of the Square if the perimeter of a square is 64cm.
Solution:
Given, perimeter = 64cm
So, Side length = perimeter/4
Side(s) = 64/4 = 16cm
From the side length we can calculate area of square by
Area =Side2
Area = 162 = 256 cm2
Area 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 cm2
Area of square is 72 cm2.
Example 3: The length of each side of a square is 5cm and the cost of painting it is Rs. 5 per sq. cm. Find total cost to paint the square.
Solution:
Given, Side length (s) = 5cm
Area of Square = s2
A = 52 = 25 cm2
For 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 m
Area 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. m
No. 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 = 6cm
From the side length we can calculate area of square by
Area = Side2
Area = 62 = 36cm2
Area of square with perimeter 24 is 36cm2.
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