Perimeter of Square: Definition, Formula, Example & Fact

Perimeter of Square: Perimeter of square is an important and fundamental concept that has its application in various situations. Simply put, the perimeter of a square is the sum of the length of all its sides. In general, the perimeter is the length of all sides of a closed figure. A square is a closed figure with four equal sides and the interior angles made between any two sides of a square is 90 degrees. Therefore, the perimeter of a square will be 4 times the length of any side of the square.

In this article, we have provided detailed information on the Perimeter of Square, Perimeter of Square Formula, Derivation, Solved Examples, FAQs and more. Read on to find out!

What is the Perimeter of Square?

The perimeter of a square is the sum of the length of all four sides. In general, the perimeter of a closed figure is the sum of the length of all sides of the closed figure. As all the sides of a square are equal, the perimeter of the square will be 4 times the length of one side.

What is Square?
A square is a quadrilateral having four equal sides. The interior angle between any two sides of a square is 90 degrees. It is a closed two-dimensional plane figure. To know more about the properties of square check the linked article.

Derivation of Perimeter of Square Formula

The perimeter of a closed figure is the length of all its sides. Therefore, the perimeter of the square will be the sum of the length of all sides of a square.

Perimeter = Sum of the lengths of 4 sides

Perimeter = Length of Side 1 + Length of Side 2 + Length of Side 3 + Length of Side 4.

Perimeter = 4 x (Length of one side)

Therefore, the Perimeter of square = 4 s

Where, s = Length of a side of the square.

Perimeter of Square Formula

Let’s consider a square with a side length of ‘a’ units. Refer to the image below:

Since the length of all sides of the square is equal, the perimeter will be:

Perimeter = a + a + a + a
Perimeter of Square (P) = 4a
Where, a is the length of one side of the square.

Also Check,

Properties of a Square

1. The four sides of a square are equal.
2. The four angles of a square are right angles i.e. 90 degrees.
3. Both the diagonals of a square are equal.
4. Both the diagonals of a square bisect each other at right angles i.e. intersect each other at right angles.
5. A square is also a cyclic quadrilateral because the four vertices of a cyclic quadrilateral are on the circumference of the circle and the four vertices of the square are also on the circumference of the circle. Being on the circumference of the circle means that if a circle is drawn from the point of intersection of both the diagonals of the square, then the four vertices of the square will be on the circumference of the circle.
6. A square is also a rectangle.
7. A square is also a parallelogram because the opposite sides of a square are equal. The opposite sides of a parallelogram are equal.

Practice Questions on Perimeter of Square

Let’s go through some solved examples on perimeter of square from below:

Question 01: Find the square of a number whose side is 3 cm.
Solution 01: The given side length of the square is 3 cm. Using the perimeter formula for square, we have,

Perimeter = 4 x Length of a side
Perimeter = 4 x 3
Perimeter = 12 cm.

Therefore the perimeter of the square with a side length of 3 cm is 12 cms.

Question 02: Find the side length of a square, if the perimeter is 24 cm.
Solution 02: The perimeter of the square is given as 24 cm. For now, let’s assume the side length of the square to be ‘a’.

We know that, the perimeter of a square = 4 × (side length)
Perimeter = 4 a
24 = 4a
a = 24/4
a = 6 cm

Therefore, the side length of a square is 6 cm.

Question 03: If the length of a side of a square wooden frame is 10cm, find the length of the wood used in the frame.
Solution 03: The length of one side of the square is given as 10 cm. The total length of wood used in the frame is nothing but the perimeter of the wooden frame.

Perimeter = 4 x Length of all sides of the wooden frame.
Perimeter = 4 x 10
Perimeter = 40 cm

Therefore, the total length of the wood used in the frame is 40 cm.

FAQs on Perimeter of Square

Check the frequently asked questions below:

Q. What is the perimeter formula?
A. Perimeter is the sum of the length of all sides of a closed figure.

Q. What is a formula of the perimeter of the square?
A. The formula for the perimeter of a square is equal to 4 times the length of each side of the square.
Perimeter = 4 x length of a side of the square.

Q. How to calculate the perimeter of a square?
A. To calculate the perimeter of a square, candidates need to add the length of all the sides of a square. However, as all the sides of a square are equal in size, the perimeter will be 4 times the length of a side of a square.

Q. What is the area and perimeter of the square?
A. The area of a square is the region covered by the square in a two-dimensional space. The area of the square is obtained by the product of the length of any two sides of a square.
On the other hand, the perimeter of a square is the sum of the length of all sides of a square.

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