AREA AND PERIMETER OF A SQUARE – MindSpark.
What is a square?
A square is a quadrilateral ( a shape having four sides) having equal sides and angles(90°each).
Perimeter of Square
Perimeter means the length of the boundary of a shape, so in a square, the perimeter will be the sum of all the sides.
Perimeter of a square = a + a + a + a = 4 × a = 4a , where ‘a’ is the side of the square.
Therefore the perimeter of a square is 4 × (side of the square).
Area of Square
The area of a square means the measure of the surface covered by the square, which is equal to the product of its two sides.
Area of square =a \times a=a^{2}
Example
1. Find the area and perimeter of a square whose side is 11 cm.
Solution:
Area of square =a \times a=a^{2}.
Here side of the square is 11 cm,
therefore area of square =11 \times 11=11^{2}=121 \mathrm{~cm}^{2}
The perimeter of a square = 4 x side = 4 x 11 = 44 cm
2. If the area of a square is 400 \mathrm{~cm}^{2}, then find the side of the square and the perimeter of the square.
Solution:
Area of square =a \times a=a^{2}. It is given that the area of the square is 400 \mathrm{~cm}^{2}. Therefore side of the square is
400=a \times a=a^{2}
⇒ 400=a^{2}
We get a = 20 cm .
Therefore the side of the square is 20 cm.
Now we’ll find the perimeter of the square
Perimeter of a square = 4 x side = 4 x 20 = 80 cm.
Explore Other Topics
Related Concepts
Frequently Asked Questions
Q1. What do you mean by the area of a square?
Ans: The area of a square means the measure of the surface covered by the square, which is equal to the product of its two sides.
Q2. What do you mean by the perimeter of a square?
Ans: Perimeter means the length of the boundary of a shape, so in a square, the perimeter will be the sum of all the sides.
Q3. What is the formula of area and perimeter of a square?
Ans: The formula of area of a square is a² and the formula of the perimeter of a square is 4a, where ‘a’ is the length of the side of the square.