Perimeter of Square

The perimeter of a square is the total distance around the shape. The perimeter of any shape is the total length covered by the shape. The perimeter of a square is calculated by adding all four sides together. When you walk all around the square playground once, that is the perimeter. Let us learn more about the perimeter of a square, its formula, and how to find the perimeter. 

The above image shows the perimeter of a square playground.

Table of Contents

• What is the Perimeter of the Square?
• Perimeter of Square Formula
• How to Calculate - Step-by-Step
• Examples
• Common Misconceptions
• Summary & Key Takeaways
• FAQs on the Perimeter of Square

What is the Perimeter of the Square?

The perimeter of a square is the sum of its sides. The entire outline of a shape is known as its perimeter. To find the perimeter, you should know the value of its sides. The square is a four-sided 2-dimensional shape. All sides of a square are equal. It is a closed shape, and opposite sides are parallel.

Perimeter of Square Formula

The perimeter of a square is the sum of all sides. The side of a square is “s”, then add all the sides, i.e., s + s + s + s = 4s. 

Perimeter of Square = 4 × Sides = 4s

Example: The side of a square is 5 units. Find the perimeter.

Solution: The side of a square is 5 units.

Perimeter of a square = 4 s

                                        = 4 × 5 units

                                        = 20 units

Therefore, the perimeter of a square is 20 units.

How to Calculate - Step-by-Step

The perimeter of the square is calculated by many parameters. Those are:

1. When the length or side is given.

2. When the area of a square is given.

3. When the diagonal of a square is given.

Let us understand each parameter in detail.

Perimeter of a Square when the length or side is given

When the length or side of a square is known, we use a general formula to find the perimeter of a square. The general formula is multiplying the side with 4. The steps involved are as follows:

Step 1: Write down the side of a square.

Step 2: Multiply the side by 4 as it contains 4 equal sides.

Step 3: Write the final answer with appropriate units.

Example: Find the perimeter of a given square.

Solution:

From the diagram, the side of a square is 8 cm.

Perimeter of square = 4 s

                                     = 4 × 8 cm

                                     = 32 cm

Therefore, the perimeter of the square is 32 cm.

Perimeter of a Square when the area is given

When the area of a square is known, the perimeter is calculated by finding the side of a square. The formula to find the area of a square is as follows:

Area of a square =  s2

Where s is the side of a square.

When the area is given, the side can be calculated with the help of below formula.

s = Area

Once the side of a square is calculated, then using the general formula perimeter can also be found out. The steps involved are as follows:

Step 1: Write down the area of the square.

Step 2: Calculate the side of a square using the formula, s = Area.

Step 3: Once the side is calculated, find the perimeter using the general formula, P = 4 s.

Step 4: Write the final answer with appropriate units.

Example: The area of the square is 36 sq. cm. Find its perimeter.

Solution: 

The area of the square is 36 sq. cm.

First, find the side of a square.

s = Area

s = 36

s = 6 cm

Now, calculate the perimeter of a square.

P = 4 s

P = 4 6

P = 24 cm

Therefore, the perimeter of a square is 24 cm.

Perimeter of a Square when the diagonal is given

When the diagonal of a square is known, then to find the perimeter, the following steps are required.

Step 1: Write down the value of the diagonal of a square.

Step 2: Calculate the side of a square using the formula

Side = 2 d2

Step 3: Now, find the perimeter of a square using the general formula, P = 4 s.

Example: The diagonal of a square is 39.59 cm. Find the perimeter of the square.

Solution: 

The diagonal of a square is 39.59 cm.

First, calculate the side of a square.

Side = 2d2

Side = 239.592

Side = 28 cm

Now, calculate the perimeter of a square.

P = 4 s

P = 4 x 28

P = 112 cm

Therefore, the perimeter of a square is 112 cm.

Examples

Example 1: If one side of a square is 12 cm, what is the perimeter?

Solution: 

Given,

Side = 12 cm

Perimeter = 4 side

Perimeter = 4 x 12 cm

Perimeter = 48 cm

Therefore, the perimeter of a square is 48 cm.

Example 2: The area of a square is 25 sq. m. Find the side and perimeter of a square.

Solution: 

Given,

Area of a square = 25 sq. m

First, find the side of a square.

s = Area

s = 25

s = 5 m

Now, calculate the perimeter of a square.

P = 4 s

P = 4 x 5

P = 20 m

Therefore, the perimeter of a square is 20 m.

Example 3: What is the perimeter if a diagonal of square is 22 cm?

Solution: 

The diagonal of a square is 22 cm.

First, calculate the side of a square.

Side = 2d2

Side = 2222

Side = 15.55 cm

Now, calculate the perimeter of a square.

P = 4 s

P = 4 x 15.55

P = 62.2 cm

Therefore, the perimeter of a square is 62.2 cm.

Common Misconceptions

• Mistakenly using the area formula to calculate perimeter or vice versa.

• The square has 4 equal sides. So, there will be no different values in lengths.

• It is important to add units in the final answer.

• The diagonal and sides of a square are not the same. There are different formulas when the diagonal is given to find the perimeter of a square.
  
  

Summary & Key Takeaways

• A square is a 4-sided quadrilateral.

• Perimeter = 4 side

• The boundary or total length of an outline is calculated by finding its perimeter.

• Mention the correct units in the final answer.

• This helps in finding the total length to fence the area, in design, construction, etc.
  
  

FAQs on the Perimeter of Square

Q1. What is the formula to calculate the perimeter of a square?

Answer: The formula for the perimeter of a square is 

                 Perimeter = 4 side

Q2. Define Perimeter.

Answer: The perimeter in maths is defined as the total length covered by any shape. 

Q3. Write the difference between the Area and Perimeter of square.

Answer: The area of a square is the space occupied by the boundary of a square. The formula for the area of a square is Area = s2. The perimeter of a square is the total distance of its boundary. The formula for the perimeter of a square is Perimeter = 4 side.

Q4. How many sides are there in the square?

Answer: There are 4 equal sides in a square and the opposite sides are parallel.

Q5. In how many ways is the perimeter of the square calculated?

Answer: The Perimeter of a square can be calculated in three ways.

                Based on the parameters given:

                1. When the length or the side of a square is given

                2. When the diagonal of a square is given

                3. When the area of a square is given