Perimeter of Square - Formula, Definition, Examples

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Author at PW

March 11, 2025

Perimeter of Square:- Understanding the perimeter of a square is an important step in building strong mathematical skills. This topic may seem simple now, but as you move to higher classes, concepts like the area and perimeter of a square, as well as other shapes, will become more advanced. Getting a good understanding of this now will make those future topics much easier to handle.

So, what is the perimeter of a square? It’s simply the total distance around the outside of the square. Since all four sides of a square are equal, you can calculate its perimeter using a simple formula: Perimeter = 4 × a, where a is the length of one side.

This idea is not only useful in maths but also in real-life situations like measuring the boundary of a garden or a room and etc. Check out the article below to learn the perimeter of square, and other details below.

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What is the Perimeter of Square?

The perimeter of a square is the total length of its boundary. Since all four sides of a square are equal, you can calculate it using a simple formula:

Perimeter = 4 × a

Here, a is the length of one side of the square. For example, if each side is 6 cm, the perimeter would be:
Perimeter = 4 × 6 = 24 cm

This makes it easy to find the boundary length of any square, whether for solving maths problems or practical tasks like fencing a garden.

Visual Representation of Perimeter of Square

Perimeter of Square

Edges (Perimeter): All four sides are highlighted to represent the perimeter of the square.
Diagonal: A line connecting opposite corners divides the square into two triangles.
Angles: Each corner forms a perfect 90°.
Vertices: These are the points where the sides meet.
Area: The inside of the square represents its total space.

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What is Perimeter and Area of Square?

While the perimeter of a square gives the total boundary length, the area of a square tells you how much space it covers. You can calculate the area using:

Area = a²

For example, if the side length is 5 cm:
Area = 5 × 5 = 25 cm²

So, the perimeter and area of a square work together to describe its boundary and the space it encloses.

Perimeter of Square Formula

The perimeter of a square can be calculated using the simple formula:

Perimeter of a square = 4 × side

area and perimeter of square

The unit of the perimeter is the same as the unit of length. For example, it can be measured in metres (m), centimetres (cm), inches (in), or any other standard unit of length.

Derivation of Perimeter of Square Formula

The perimeter of a square is the total distance around its boundary. To calculate the perimeter, you simply add up the lengths of all four sides of the square.

Using the general formula for the perimeter of a polygon:

Perimeter = Sum of all sides

For a square, since all four sides are of equal length:
Perimeter of a square = side + side + side + side
= 4 × side

Thus, the formula becomes:
Perimeter of a square = 4s units

Here, s represents the length of one side of the square.

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Perimeter of Square Using Area

The area of a square refers to the amount of space it occupies. The formula to calculate the area of a square is:

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

Here, side (s) represents the length of one side of the square.

If the area is given, the length of a side can be determined using:
side = √Area

Once the side length is known, the perimeter of the square can be calculated as: Perimeter = 4 × side = 4 √Area units

This means you can easily find the perimeter of a square if its area is provided.

Example: If the area of a square is 16 sq. cm, find its perimeter.

Using the formula: Perimeter = 4 √Area = 4 √16 = 4 × 4 = 16 cm

So, the perimeter of the square is 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

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Important Facts on Perimeter of Square

1. Equal Sides

All four sides of a square are equal in length. This is a fundamental property of a square, making its perimeter easy to calculate.

2. Formula for Perimeter

The perimeter (P) of a square can be calculated using the formula:

This formula is simple because all four sides of the square have the same length.

3. Units of Measurement

The perimeter is measured in the same units as the side of the square (e.g., centimeters, meters, inches). If the side length is given in centimeters, the perimeter will also be in centimeters.

4. Relationship to Area

The area of a square is related to its perimeter. If you know the area, you can find the side length by taking the square root of the area:

Then, you can calculate the perimeter by multiplying the side length by 4.

5. Dependence on Side Length

The perimeter of a square is directly proportional to its side length. If the side length increases, the perimeter increases by the same factor.

6. Diagonal and Perimeter

If the diagonal of a square is given, you can find the perimeter by first calculating the side length using the relationship:

Then, apply the perimeter formula.

7. Perimeter of a Square vs. Other Shapes

The perimeter of a square is easier to calculate than for many other polygons since all sides are equal. For rectangles, triangles, or irregular polygons, you need to add up the lengths of each individual side.