Perimeter of Square - Formula, Definition, Examples

Perimeter of square is one of the most important topics in Maths. A square is a four-sided geometrical shape, and all its sides are of the same length. Using the perimeter of square formula, which is 4 x a (a is the length of a side), we can calculate the total distance around the square. Learning the perimeter of square is helpful not only in solving maths questions but also in understanding many real-life situations.

For example, the perimeter of square formula makes it easy to solve real-life problems like finding the boundary of a square garden, the border of a floor tile, or even the frame of a photo. So, let's learn what is the perimeter of square in detail and its formula, along with examples to practice.

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What is the Perimeter of Square?

Before using the formula to solve questions, it is important for you to understand what is the perimeter of square means. Perimeter of square means the total distance covered by the outer boundary of the shape. For example, if a floor is in a square shape and has four equal sides, then if you walk once around it, the distance you cover is called its perimeter.

Therefore, to find the perimeter of square, all you need to do is just add all its four sides together. Since each side has the same length, instead of adding again and again, you can also multiply the length of one side by 4, which makes it very easy to calculate.

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Perimeter of Square Formula

Understanding and remembering the perimeter of square formula is very easy. Since a square has four equal sides, the total length around it can be written as:

Perimeter of Square Formula (P) = 4 × side

This means if one side of the square is ‘a,’ then the perimeter is 4 times ‘a.’ For example, if each side of a square is 6 cm, and you need to find its perimeter, then using the perimeter of square formula, you will do 4 × 6 = 24 cm.

So, the perimeter of square formula is useful because it gives the answer quickly without adding the sides one by one while solving tricky or advanced questions.

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How to Find Perimeter of a Square?

There are three main ways to learn how to find perimeter of a square. The method you use depends on the information given in the question. Let’s understand how to find perimeter of a square using different methods:

1. How to Find Perimeter of a Square Using Side Length?

This is the easiest and most common method to find the perimeter of square. As you learned, a square has four equal sides, and if the length of one side is given, you can find the perimeter by multiplying it by 4.

For example, if one side of the square is 5 cm, then: Perimeter = 4 × 5 = 20 cm.
So, the total boundary of the square is 20 cm. It is important to add the units like cm, m, inches, etc. to the final answer.

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2. How to Find Perimeter of a Square Using the Diagonal

In some questions, in place of the side, the length of the diagonal, which is the corner to the opposite corner, is given. In this question, you can still find the perimeter.

• Use the formula to find one side: side = diagonal ÷ √2.

• Multiply the side length by 4 to get the perimeter.

For example, if the diagonal of a square is 14 cm, then the side = 14 ÷ √2 = 9.9 cm (approx.). Now using the Perimeter of Square Formula = 4 x side = 4 × 9.9 = 39.6 cm.

3. How to Find Perimeter of a Square Using Area

The area of a square means the space covered inside the square. For example, if you draw a square on paper and color the inside part, the colored space is called its area.

Now, sometimes in questions, the area of the square is given instead of the side length. In that case, we can still find the perimeter. Here’s how:

• Find the side length by taking the square root of the area (side = √area).

• Once you find the length, multiply it by 4 to calculate the perimeter.

• For example, if the area of a square is 64 cm², then you can find the side like this: √64 = 8 cm.

• After that, put the value of the side in the Perimeter of Square Formula = 4 × 8 = 32 cm.

Also read: What is a Polyhedron—Definition, Types, and Examples

Perimeter of Square vs Area of Square: Are Both the Same?

Many students confuse the perimeter of square with the area of square, but it is important to understand that they are not the same. The perimeter of square is the outside boundary of the square, while the area is the space it covers from inside. Both are important concepts in math and are used for different scenarios.

• Perimeter of Square: It is the total distance around the square. The perimeter of square formula is P = 4 × side. It is measured in length units like cm, m, or inches.

• Area of a Square: It is the total surface or region covered inside the square. The area of a square is calculated by using the formula: A = side × side (s²). It is measured in square units like cm², m², or in².

To understand it better, check the visual representation of the Perimeter of Square given below:

Solved Perimeter of Square Examples

Understanding becomes easier and clearer when you go through the perimeter of square examples. By solving these questions step by step, you will learn how to use the perimeter of square formula in different scenarios.

Example 1: Find the perimeter of a square whose side is 7 cm.

Solution:

Perimeter of Square = 4 × side
= 4 × 7 = 28 cm
So, the perimeter of the square is 28 cm.

Example 2: A square-shaped garden has a side of 12 m. How much fencing is needed to cover it completely?

Solution:

Using Perimeter of Square Formula = 4 × side
= 4 × 12 = 48 m

Therefore, 48 metres of fencing will be required to completely cover the garden.

Example 3: The diagonal of a square is 10 cm. Find its perimeter.

Solution:

Side = diagonal ÷ √2
= 10 ÷ √2 = 7.07 cm (approx.)

So, Perimeter of Square = 4 × 7.07 = 28.28 cm (approx.)

Example 4: The area of a square is 81 cm². Find its perimeter.

Solution:

Side = √area = √81 = 9 cm
Perimeter = 4 × side = 4 × 9 = 36 cm

So, the perimeter of square is 36 cm.

Example 5: A square tile has a side of 15 cm. A border is to be made around it. Find the length of the border.

Solution:

Perimeter of Square Formula = 4 × side = 4 × 15 = 60 cm

So, the border will be 60 cm long.

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