how to find the perimeter of a square

Perimeter of Square

The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical object is calculated by finding the distance around that object. For a square, the perimeter can be calculated by finding the sum of all the sides. Let us have a look at the article in order to understand the concept in a better way.

1.	What is the Perimeter of Square?
2.	Derivation of Perimeter of Square Formula
3.	How to Calculate Perimeter of a Square
4.	FAQs on Perimeter of Square

What is the Perimeter of Square?

A 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 is as, mathematically expressed as;
Perimeter of square, (P) = 4 × Side

perimeter of square formula

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 the 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 Calculate 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

We generally find the perimeter for this case 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 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 1: If the perimeter of a square is 64 units, find its side.

Solution:

To Find: Side length of square

Given: Perimeter of square = 64 units

Using the perimeter of a square formula,
Perimeter of square = 4 × side units
Substituting values, we get,
64 = 4 × side
⇒ Side = 64/4 = 16 units

Answer: The side length of the given square measures 16 units.
Example 2: The area of a square is given as 225 square units. Using the perimeter of a square formula, calculate its perimeter.

Solution:

To find: Perimeter of given square

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 of square, P = 4 × side units
⇒ P = 4 × 15 = 60 units

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

go to slidego to slide

Want to build a strong foundation in Math?

Go beyond memorizing formulas and understand the 'why' behind them. Experience Cuemath and get started.

Book a Free Trial Class

Practice Questions on Perimeter of Square

go to slidego to slide

FAQs on Perimeter of Square

What is Perimeter of Square in Math?

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

☛Also Check:

Perimeter Formulas
Area Formulas

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 Find 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.

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: 4√area.

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), and meters(m).

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. Try Cuemath's perimeter of square calculator now and get your answers just by a click.

☛Check now perimeter of squares worksheets for more practice.

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.