Perimeter of a Square Formula

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Perimeter of Square

The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical shape is calculated by finding the distance around that shape. For a square, the perimeter can be calculated by finding the sum of all the sides. Since all four sides are equal, it is four times the length of each side of a square.

What is the Perimeter of Square?

The perimeter of any shape is either a path that encompasses/surrounds/outlines a shape (in two dimensions) or its length (one-dimensional). The perimeter of a square can be calculated by adding the length of all its sides.

Perimeter of Square Formula

The formula to calculate the perimeter of a square can be mathematically expressed as;
Perimeter of square, (P) = 4 × Side

Example: Calculate the perimeter of a square with each side measuring 7 units.

Solution: Given: Side length of square = 7 units.
We know, using the perimeter of a square formula,

Perimeter of square = 4 × Side
⇒ 4 × 7 = 28 units

Derivation of Perimeter of Square Formula

The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since all sides of a square are equal for a square, with each side measuring “s” units, perimeter will thus be given as,

Perimeter of square = s + s + s + s
⇒ Perimeter of square = 4s, where “s” is the side length of the square.

How to Find Perimeter of a Square?

The perimeter of the square can be calculated following different methods depending upon the known parameters. This section will cover the method using,

  • Side length
  • Diagonal
  • Area

Perimeter of Square Using Side Length

In this case, we generally find the perimeter by multiplication of side length with 4. To find the perimeter of a square using the side length, we can follow the steps given below,

  • Step 1: Note down the measurement of the side.
  • Step 2: Multiply the noted length with 4.
  • Step 3: Express the obtained result with the appropriate unit.

Perimeter of Square Using Diagonal

The perimeter of the square can also be calculated if the length of its diagonal is known to us. To find the perimeter of a square using the diagonal, we can follow the steps given below:

  • Step 1: Note down the measurement of the diagonal of the square.
  • Step 2: Calculate the side length using the diagonal.
    Side = diagonal/√2 = √2 × diagonal/ 2
  • Step 3: Multiply this obtained value of side length, (√2 × diagonal/ 2) by 4 and express the answer in units.
    Perimeter = (√2 × diagonal/2) × 4 = (2√2 × diagonal) units.

Perimeter of Square Using Area of Square

We can find the perimeter of the square given the area. To find the perimeter of a square using the area, we can follow the steps given below:

  • Step 1: Note down the area of square.
  • Step 2: Calculate the side length using the area.
    Side = √area
  • Step 3: Multiply this obtained value of side length, (√area) by 4 and express the answer in units.
    Perimeter = (√area) × 4 = 4√area units.

Let us have a look at a few solved examples to understand the perimeter of the square better.

Perimeter of Square Examples

Example 2: The area of a square is given as 225 square units. Using the perimeter of a square formula, calculate its perimeter.

Solution:

Given: Area of square = 225 square units.

We know, area of a square = (side)2 square units
⇒ 225 = (side)2
⇒ side = 225 = 15 units

Now, using perimeter of a square formula,
Perimeter, P = 4 × side units
⇒ P = 4 × 15 = 60 units

Answer: The perimeter of the given square = 60 units.

Example 3: If the diagonal of a square measures 3√2 inches, what will be the perimeter of square?

Solution:

Given: Diagonal of square = 3√2 inches.

As we know that in terms of diagonal, the perimeter of square formula is P = (2√2 × diagonal) units.
⇒ P = (2√2 × 3√2) inches
P = 6 × 2 inches
p = 12 inches

Answer: The perimeter of the given square = 12 inches.

FAQs on Perimeter of Square

What is Perimeter of Square in Math?

The perimeter of a square in math is the total length around its boundary. The perimeter formula for square is expressed as the sum of all the sides. It is represented as P = 4 × side units.

What is the Formula of Perimeter of Square?

The perimeter of a square is defined as the length that its boundary covers. The formula to calculate the perimeter of a square is given as: P = 4 × side.

How to Calculate Perimeter of Square?

The perimeter of a square can be calculated by finding the total sum of all its sides. Since, the measure of all the sides of a square is equal, to calculate the perimeter of a square we can simply multiply 4 with its side length.

What is the Area and Perimeter of Square?

The area of a square is the space occupied within the boundary of the square. It is calculated by using the formula: Area = (side × side) square units. On the other hand, the perimeter of square is the total length of its boundary. It can be found by adding all four sides of the square or by multiplying any one side by 4. The formula to find perimeter of a square is (4 × side) units.

How to Find the Side Length of a Square When the Perimeter is Given?

The perimeter of a square is given as, P = 4 × side. On rearranging the above formula to calculate the side length of the square when the perimeter is given, we get, side = P/4. Therefore, the side length of a square can be calculated by dividing the given perimeter by 4.

How to Find Perimeter of Square When Area is Given?

The area of a square can be calculated using the formula, area = side × side. On rearranging this formula to calculate the side length of the square using the area, we get, side = area. Since the perimeter of a square is given as: 4 × side, we can calculate the perimeter of a square when the area is given using the formula: 4area.

What is the Unit of Perimeter of Square?

The perimeter of a square is the total distance around its boundary, or the lengths of its sides added together. Perimeter (P) is measured in units such as inches(in), yards(yd), millimeters(mm), centimeters(cm), meters(m), etc.

How to Use the Perimeter of Square Calculator?

Perimeter of square calculator is used to do fast calculations and get the desired answer of the perimeter of square quickly. To calculate the perimeter of a square using a calculator we need to enter certain specific parameters such as the side length of a square.

How to Find Perimeter of Square When Diagonal is Given?

The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.

Perimeter of a square – Definition with Examples

Perimeter of a Square

A square is a type of rectangle in which the adjacent sides are equal. In other words, all the sides of a square are equal.

Following are the properties of a square: 

(i) All the angles in a square are the same and equal 90º. 

(ii) All the sides of a square are equal.

Perimeter of a square

The perimeter of a square is the total length of all the sides of the square. Hence we can find the perimeter of a square by adding all its four sides.

The perimeter of the given square is a + a + a + a. Since all sides of a square are equal, we only need one side to find its perimeter.

The perimeter of the given square is:  

a + a + a + a = 4  a units.

Hence, the formula of the perimeter of a square = 4 × (length of any one side).

Tricky math problems with the squares:

Type I: Finding side length when only the perimeter is given.

Example 1. If the perimeter of the given square is 12 cm. What will be the length of its side?

Solution: Given, the perimeter of the square is 12 cm.

Let the side length be ‘a’ cm.

We know that, the perimeter of a square = 4 × (side length)

12=4×(a)

a = 3 cm

Type II: Finding sides using square properties.

Example 2.If a = 4 cm in the given square. Find b, c. and d.

Solution: Given that side a = 4 cm.

To find side b, c, and d  we use the property of the square which states that all the sides of a square are equal.

Therefore, a = b = c = d = 4 cm

Type III: Finding perimeter when one of the sides is given.

Example 3. One of the sides of a square is 5 cm. What will be its perimeter?

Solution: Given, one side of the square is 5 cm.

We know that, the perimeter of a square = 4 × (side length)

= 4×(5)

= 20 cm

Example 4. The length of a side of the square wooden frame is 5 cm. Find the total length of the wood used in the frame.

Solution: Given, the length of a side of this wooden frame is 5 cm.

As we know, the perimeter of a square = 4× (side length)

= 4  (5)

= 20 cm

Hence, the total length of the wood used is 20 cm.

  Fun Facts Squares are one of the three most basic shapes on the earth. The other two are circles and triangles.

What is Perimeter of a Square?

The perimeter of any closed geometrical object is defined as the distance around that object. The perimeter of a square is the distance covered by its four sides.  Perimeter surrounds or outlines the shape in a two-dimensional plane.

Since all the sides of a square are equal, therefore, the perimeter of square will be 4 times its side, i.e. 4 × Side. It is measured in units, such as m, cm, in, ft, etc.

Perimeter of Square Formula

The formula to find the perimeter of a square is given below:

Perimeter of Square (P) = 4 × Side

Example: If length of side of square is 3cm, then find its perimeter.

Perimeter of square = 4 x side = 4 x 3 = 12 cm.

Derivation of Perimeter of Square Formula

The perimeter of the square is defined as the total length of the boundary of a square. We need to add all the sides of square to find its perimeter. By the formula of perimeter of polygon, we know;

Perimeter = sum of all sides

Perimeter of square = Sum of the lengths of 4 sides

= side + side + side + side

= 4 × side

Therefore, the perimeter of Square = 4s units

Where, s = Length of a side of the square

How to Find Perimeter of Square?

We have already learned to calculate the perimeter of the square using the formula,

Perimeter = 4 × side

But if the length of the side of square is not given, then we can calculate the perimeter of square, if two we are given with either of two details:

  1. Length of diagonal of square
  2. Area of square

Let us figure out, how we can find the perimeter using diagonal and using area.

Perimeter of Square Using Diagonal

As we know, a square is regular polygon that has all sides equal. Also, all the four angles of square are 90 degrees. Thus, we get the length of diagonal of square, using Pythagoras theorem, as:

Diagonal = Side.√2

Thus, the side of square can be written as:

Side = Diagonal/√2

or

Side of square = √2(Diagonal/2)

As we know,

Perimeter of square = 4 x side = 4 x √2(Diagonal/2)

Perimeter of square = 2√2(Diagonal) units.

Hence, we can find the perimeter using diagonal of square.

Example: Find the perimeter of square, whose diagonal length is 10 cm. By using the above formula, we have; Perimeter = 2√2(Diagonal) = 2√2(10) = 20√2 cm.

Perimeter of Square Using Area

The area of a square is defined as the space occupied by the square. The formula for area of square is given by:

Area of a Square = side × side = side² square units

where “s” is the length of one side.

Now, we can write, side of the square w.r.t. area,

side = √Area

Hence, the perimeter of square will be:

Perimeter = 4 x side = 4 √Area units.

Thus, we can find the perimeter of a square given its area.

Example: If area of square is 16 sq.cm. Find its perimeter. Using the above formula, we have; Perimeter = 4 √Area = 4 √16 = 4 x 4 = 16 cm.

Solved Examples on Perimeter of Square

Question 1: Find the perimeter of a square whose side is 5 cm.

Solution:

Given:

Side, s = 5 cm

The formula to find the perimeter of a square is given by:

The perimeter of Square = 4s units

Substitute the value of ‘s’ in the perimeter formula,

P= 4 × 5 cm

P = 20 cm

Therefore, the perimeter of square = 20 cm

Question 2: Calculate the perimeter of a square having a side of 16 cm.

Solution:

Given,
Side of the square = a = 16 cm

Perimeter of a Square = 4a
= 4 × 16
= 64 cm

Question 3: If the perimeter of a square is 92 cm, find its side.

Solution:

Perimeter = 4 × side

Or, Side of Square = ¼ × perimeter

So, side of the square = 92/4 = 23 cm

Practice Questions on Perimeter of square

  1. What is the perimeter of square, whose side is equal to 11 cm?
  2. If length of side of square is 5.5 cm, then find its perimeter.
  3. The length of diagonal of a square is equal to 9 cm. Find its perimeter. (Use: √2 = 1.414)
  4. If the area of square is 100 sq.in., find its perimeter.

Frequently Asked Questions

What is the Perimeter of a Square?

The perimeter of a square is defined as the total distance around the outside of the square. So, it can be said that a square’s perimeter is its total boundary.

How to Find the Perimeter of a Square?

To calculate the perimeter of a square, add all the sides of it. There are 4 sides of a square which are all equal in length. The sum of the sides will give its perimeter. We can use also find the perimeter of square if the length of diagonal or area of square is given to us.

What is the Formula for the Perimeter of a Square?

The formula for the perimeter of a square is, P = Side + Side + Side + Side

Or, P = 4 × Side

What is the unit of perimeter of square?

Perimeter of square is the total distance enclosed by its sides. Perimeter is measures in units such as meters (m), centimeters (cm), inches (in), etc.

What is area of a square?

The area of a square is the region that the square covers in a two-dimensional space. The area of a square can also be defined as the number of square units it takes to fill the square.

How to find the Area and Perimeter of a Square

Perimeter of a Square

Perimeter and Area of Square

The formula of perimeter and area of square are explained step-by-step with solved examples.

If ‘a’ denotes the side of the square, then, length of each side of a square is ‘a’ units

Perimeter of square = AB + BC + CD + DA

                              = (a + a + a + a) units

                              = 4a units

● Perimeter of the square = 4a units 

We know that the area of the square is given by

Area = side × side

A = a × a sq. units

Therefore, A = a² square units

Therefore, a² = A Here, a is the side of the square.

Therefore, a² = √A

Therefore, side of the square = √Area


● Side of the square = P/4 units 

● Area of the square = a × a = (P/4)² sq. units 

● Area of square = 1/2 × (diagonal)² sq. units 

● Length of the diagonal = √(a² + a²) = √(2a²^2) = a√2 units

Worked-out examples on Perimeter and Area of the Square:

1. Find the perimeter and area of a square of side 11 cm.

Solution:

We know that the perimeter of square = 4 × side

Side= 11 cm

Therefore, perimeter = 4 × 11 cm = 44 cm

Now, area of the square = (side × side) sq. units

                                        = 11 × 11 cm²

                                        = 121 cm² 

2. The perimeter of a square is 52 m. Find the area of the square. 


Solution:

Perimeter of square = 52 m

But perimeter of square = 4 × side

Therefore, 4 × side = 52 m

Therefore, side= 52/4 m = 13m

Now, the area of the square = (side × side)

Therefore, area of the square = 13 × 13 m² = 169 m².

3. The area of a square is 144 m². Find its perimeter. 

Solution: 

Area of square = side × side 

Given; area of square = 144 m²

Therefore, side² = 144 m²

Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 2 × 2 × 3 m = 12 m

Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m

4. The length of the diagonal of a square is 12 cm. Find its area and perimeter. 

Solution: 

Diagonal of a square = 12 cm 

Area of square = 1/2 (d)² 

                         = 1/2 (12)² 

                         = 1/2 × 12 × 12 

                         = 72 

Side of a square = √Area

                           = √72

                           = √(2 × 2 × 2 × 3 × 3) 

                           = 2 × 3√2

                           = 6 × 1.41

                           = 8.46 cm

Perimeter of square = 4 × 8.46 = 33.84 cm

5. The perimeter of a square courtyard is 144 m. Find the cost of cementing it at the rate of $5 per m². 

Solution: 

Perimeter of square courtyard = 144 m

Therefore, side of the square courtyard = 144/4 = 36 m

Therefore, area of square courtyard = 36 × 36 m² = 1296 m² 

For 1 m², the cost of cementing = $5 

For 1296 m², the cost of cementing = $1296 × 5 = $6480

Solved Examples

Below are the Perimeter of Square Formula examples:

Problem 1:

Preeti takes three rounds of a square park of side 70m. Find the distance traveled by Shaina.

Solution: Side of the square park is 70 meter.

We know, the perimeter of a square = sum of all the sides

                                   = 70 x 70 x 70 x 70 meters

                                   = 4 x 70 meters

                                   = 280 meters.

Therefore, the boundary of the square park measures 280 meters.

If Preeti takes three rounds of the park, then the total distance traveled by Preeti

= 3 x 280 meters

= 840 meters.

Problem 2: 

The lid of a square box of side 50cm is sealed with tape. What is the length of the tape?

Solution: 

Length of the side of the square box is 50cm. 

The length of the tape is equal to the perimeter of the box

The perimeter of the box = 4 x side

                                              = 4 x 50 cm

                                              = 200 cm.

Thus, the length of the tape is 200cm.

Problem 3:

If the perimeter of a square is 20m, then what is the side of the square?

Solution:

We know, 

Perimeter = 4 x side

Side = Perimeter / 4

        = 20 / 4 cm

        = 5 cm.

Problem 4: 

What is the Perimeter of a square and also find the cost of fencing a square park of 250 meters at the rate of Rs 20 per meter.

Solution: To find the cost of fencing a square park we need to find out the length of the boundary of a square park.

The perimeter of a square = 4 x sides

 If the side of the square park is 250 meters then,

 The perimeter of a square = 4 x 250

                                                 = 1000 meters.

The cost of fencing 1 meter is Rs 20 

So, the cost of fencing 1000 meters will be 1000×20  i.e,  20,000.

Therefore the cost of fencing a square park of sides 250 meters is Rs 20,000.

Finding the Perimeter of the Square using its Area 

Suppose the question does not specify the side length of the square. Instead, it gives you the area of the square and asks you to find the perimeter. 

Then, you can find the perimeter of the square by using the formula of the area of a square. Follow the steps mentioned below to understand how to determine the perimeter,

  1. Read the question carefully and note down the area of the square. 
  2. You can use the area to find the side length of the square. Here’s how: 

Area of square (A)= Side × Side 

So, Side = √A

  1. Once you have obtained the side length, you can put its value in the formula of the perimeter of the square. 

Perimeter = 4 × √area 

Finding the Area of Perimeter using its Diagonals 

Like the above question, some questions will only specify the diagonal length of the square instead of the side length. In such cases, you can follow the steps mentioned below to find the perimeter of the square.

  1. Go through the question thoroughly and note down the diagonal length. 
  2. Use the diagonal length to find the side length of the square using the formula: 

Side = diagonal/√2 

  1. Then apply the length of the side, obtained in the above step, in the formula of the perimeter of the square. You will get, 

Perimeter = 4 × diagonal/√2 

This way, you can find the perimeter of the square using only the length of the diagonals. By learning these formulas, you will be able to solve any question, based on the perimeter of a square, asked in your math exam.

FAQs (Frequently Asked Questions)

1. What is the best place to learn the Perimeter of Square?

Vedantu is the best place to learn the Perimeter of Square. We provide you with reliable content curated by some of the best subject experts who have years of experience. You can learn the Perimeter of Square from our website or download our mobile app from the app store for iOS and play store for android smartphones. Moreover, you can find plenty of study materials for different subjects such as math, chemistry, biology, and physics only on Vedantu for absolutely free. Learn topics like integers, number systems, odd and even numbers, and much more only from Vedantu’s online learning platform.

2. How to remember the formula of the perimeter of the square?

Remembering the formula of the perimeter of a square is not that difficult. The perimeter of a square is the addition of all its side lengths. However, in some questions, the side length will not be given. Instead, the length of the diagonals will be known. Also, some questions even ask you to find the perimeter of the square using its area, which is given. So, you have to understand and memorize all the formulas to ensure that you do not make any mistakes in the exam. Below are all the formulas of the perimeter of a square: 

  • Side length: Sum of all sides 
  • Diagonal length: 2.√2 × length of diagonal 
  • Area: 4√area

3. Is it important to learn the Perimeter of Square?

Yes, it is important to learn the perimeter of a square. By learning the formula of the perimeter of a square, you will be able to solve a number of mensuration questions. The perimeter of a square will make it easier for you to understand the area as well. It is one of the basic formulas of math that come in handy throughout your academic years. Once you remember all the formulas of the Perimeter of Square, you will be able to solve any type of question that is asked in the exam.

4. How can I calculate the perimeter of a square?

Calculating the perimeter of a square will be much easier if you know all the formulas. You have to carefully read the information provided in the question before you start calculating the perimeter of the square. Check whether the question has specified the side lengths or the diagonal length of the square. Moreover, some questions also mention the area of the square that you can use to find the perimeter. You have to memorize all the formulas of the perimeter of the square to solve such questions.

5. Can I find the side length of a square when its perimeter is given?  

Yes, you can find the side length of a square when its perimeter is given. All you have to remember is the formula of the perimeter of a square using side lengths. Here’s how you can determine the side lengths: 

Let the side of the square be X. We know, 

The perimeter of square (P) = 4 × X

By rearranging the above formula, we can get, 

X = P/4 

That is how you can determine the length of the sides of a square when its perimeter is given in the question. 

Question 1: Find the perimeter of a square each of side 5 cm.

Solution:

Length of each side of the square = 5 cm

Perimeter of the square = sum of all sides = 5 + 5 + 5 + 5 = 20 cm

Thus, perimeter of square = 20 cm

Question 2: Find the length of sides of a square with a perimeter of 48 cm.

Solution:

Given perimeter of the square = 48 cm

Lets length of each side of the square = ‘a’ cm

Therefore, perimeter = 4a cm

Therefore, we can write:

4a = 48 cm

a = 12 cm

Thus, length of each side of square is 12 cm.

Question 3: Find the perimeter of a square whose length of diagonal is 4√2 cm.

Solution:

Given, the length of a diagonal square = 4√2 cm.

Let the length of each side of the square = a cm.

Thus, applying the Pythagoras theorem, the length of diagonal = √(a2+a2) = a√2 cm

So, we can write:

a√2 = 4√2

a = 4 cm

Thus, the perimeter of square = 4a = 4 × 4 = 16 cm

Question 4: Find the sum of adjacent sides of a square given perimeter of the square is 12 cm.

Solution:

Given the perimeter of the square = 12 cm

Considering length of each side = ‘a’ cm, the perimeter = 4a cm

Thus, we can write:

4a = 12

a = 3 cm

Since adjacent sides of a square are having the same length, we can write the sum of any adjacent sides of the square = a + a = 2a 

Therefore, the sum of adjacent sides of the square = 2 × 3 = 6 cm

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