Perimeter of a Square
We will discuss here how to find the perimeter of a square. Perimeter of a square is the total length (distance) of the boundary of a square.
In a square all the sides are of equal lengths.
Hence, perimeter of a square = 4l
We know that all the sides of a square are equal.
Perimeter of the square ABCD
= AB + BC + CD + AD
= 2 cm + 2 cm + 2 cm + 2 cm
= (2 × 4) cm
= 8 cm
Perimeter of a square is 4 times of s side.
Perimeter of a square = 4 × length of a side.
A square is a four sided figure in which
● all the four sides are equal (length = breadth)
● all the angles are equal to 90° (right angle)
1st method:
Perimeter of a square PQRS
= side + side + side + side
= 5 cm + 5 cm + 5 cm + 5 cm
= 20 cm
2nd method:
Perimeter of a square = 4 times side
= 4 × side
= 4 × 5 cm
= 20 cm
Therefore, Perimeter of a square = 4 × length of one side
Word Problems on Perimeter of a Square:
Let us consider some of the examples on perimeter of a square:
1. Each side of a square is 2.5 cm. Find its perimeter.
Solution:
Side = 2.5 cm
Therefore, perimeter of a square = 4 × length of a side
= (4 × 2.5) cm
= 10 cm
2. A rope of length 96 m was used to fence a square garden. What is the length of the side of the garden?
Solution:
Perimeter of the garden = Length of the rope = 96 m
We know that perimeter of a square = 4 × length of a side
So, 4 × length of a side = 96 m
Length of a side = \(\frac{96}{4}\) m = 24 m
Therefore, length of the one side of the square shape garden is 24 m.
3. Find the perimeter of a square shaped playground whose each side length 12 m.
Solution:
We know a square has four equal sides. So, we can easily calculate the perimeter of a square.
The formula for finding the perimeter of a square is:
P = 4 × length of a side
= 4 × 12 m
= 48 m
4. Each sides of a paper sheet is 14 ft. Find its perimeter.
Solution:
Given: Side length is 14 ft.
Perimeter of a square is = 4 × side
= 4 × 14 ft
= 56 ft
5. Find the perimeter of the square PQRS whose one side is 10.5 m.
Solution:
Side of the square = 10.5 m
Perimeter of the square = 4 × side
= 4 × 10.5
= 42 m
6. Find the perimeter of the square PQRS whose one side is 4 cm.
Solution:
The perimeter of the square
= 4 × side
= 4 × 4 cm
= 16 cm
7. The perimeter of a square is 20 cm. Find the length of each side of the square.
Solution:
Perimeter of the square = 4 × side of the square
i.e. 4 side of the square = 20 cm
But we have 4 × 5 = 20 (Note: 20 × 4 = 5)
Therefore, side of the square = 5 cm
8. How to find the perimeter of a square?
Find the perimeter of the figure:
Solution:
A square has four sides.
To find the perimeter of a square, we measure all the four sides of the figure and add them together.
In the above given figure, all the sides length = 4 cm
Therefore, perimeter of the square = 4 cm + 4 cm + 4 cm + 4 cm
= 16 cm
Worksheet on Perimeter of a Square:
1. Find the perimeter of squares having sides as follows.
(i) 8 cm
(ii) 6 cm
(iii) 10 cm
(iv) 12 cm
(v) 15 cm
Answer:
1. (i) 32 cm
(ii) 24 cm
(iii) 40 cm
(iv) 48 cm
(v) 60 cm
2. The perimeter of a square photo frame is 12 cm. What is the length of its side?
Answer:
2. 3 cm
3. A square has a perimeter of 24 cm. What is the length of each side?
Answer:
3. 6 cm
4. Find the perimeter of each of the following square using formula:
Answer:
4. (i) Perimeter of the square 24 cm.
(ii) Perimeter of the square 28 cm.
(iii) Perimeter of the square 24 cm.
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