Perimeter of Square Formula- Derivation, Unit, Examples

Perimeter of Square

The perimeter of Square is the length of the square-shaped object’s boundary as measured in a plane that is encircled by that shape. The formula of the perimeter of Square and its use in a variety of sectors and daily life. Since a square is a polygon with four equal sides, the perimeter of square is determined by adding the lengths of all its sides in a two-dimensional space. Here, we’ve included a thorough explanation of the perimeter of square, its formula, and its derivation, along with solved examples.

What is the Perimeter of a Square?

Before learning about the perimeter of a Square, we must have an idea about the perimeter. Perimeter is the total length of the boundary of any closed geometrical shape. A path that surrounds a shape is the perimeter of any shape (in two dimensions). The perimeter of a Square is the distance occupied by its four equal sides. A square’s perimeter can be determined by adding the lengths of all its sides.

Perimeter of Square Formula

A Square is a two-dimensional geometrical closed figure with four equal sides and the internal angles formed by any two square sides are 90 degrees. We can determine the perimeter of a Square by adding the length of Four sides The formula for calculating the perimeter of a square is as follows:

Perimeter of Square Formula Derivation

The use of the Perimeter of Square formula is very frequent in our daily life. Suppose, a farmer must know the expense of fencing his land in order to protect his crops from ruminant animals. To determine the cost of fencing, he must first determine the perimeter of his area.

The perimeter of the square is defined as the total length of a square’s boundaries. We shall find the sum of all of the square’s sides to calculate its perimeter. Now, assume a square having sides of  ” a ” units. the perimeter will be given as,

The perimeter of square = Sum of the lengths of 4 sides

perimeter of the square = Length of Side 1+Length of Side 2 +Length of Side 3 +Length of Side 4.

Or, Perimeter of Square = a + a + a + a unit 

Or, Perimeter of square = 4 x (Length of one side)

Or, Perimeter of the Square. (P) = 4 ×a unit.

वर्ग का परिमाप का सूत्र

वर्ग का परिमाप (Perimeter) निकालने के लिए निम्नलिखित सूत्र का उपयोग किया जाता है:

परिमाप (Perimeter)=4×भुजा (Side Length)

अगर वर्ग की एक भुजा

a है, तो इसका परिमाप

4×a होगा।

उदाहरण: अगर वर्ग की भुजा 5 सेंटीमीटर है, तो इसका परिमाप

4×5=20 सेंटीमीटर होगा।

यह सूत्र वर्ग के सभी भुजाओं के लिए समान होने के कारण उपयोगी है, क्योंकि वर्ग के सभी भुजाएं बराबर होती हैं।

Perimeter of Square unit

A square is a closed object with four equal sides, and the internal angles formed by any two square sides are 90 degrees. As a result, the perimeter of a square is four times the length of any of its sides. Because all of the sides of a square are equal, the perimeter of the square will be 4 times its side, i.e. 4 ×Side.

It is measured in units such as meters, centimeters, inches, feet, etc

How to find the Perimeter of Square

We can find the perimeter of the square by adding all four equal sides. The perimeter of the square, (P) = 4 × Side units.

But if the square’s side length is not provided, we may still determine the square’s perimeter if we are given one of two details:\

• Length of diagonal of the square
• Area of square

Let’s explore how to calculate the perimeter using the diagonal and the area.

Perimeter of Square Using the Area

The space that a square occupies is referred to as its area. Given the area, we can calculate the square’s perimeter. Using the area, one may determine a square’s perimeter. The following is the formula for square area:
The  area of square=  side x side = side² square units
side = √Area units.
As a result, the perimeter of Square will be:

Perimeter of Square Using Diagonal

If we know how long the square’s diagonal is, Using the diagonal of a square, we can also determine the perimeter of a Square. Earlier we know that a square is a regular polygon with equal sides. Additionally, the square’s four angles are all 90 degrees. By applying Pythagoras’s theorem, we may determine the length of a square’s diagonal as follows:

Diagonal = Side.√2
The side of a square can therefore be expressed as follows:
Side = Diagonal/√2
The side of a square can therefore be expressed as follows:

Perimeter of Square Formula Based Examples

Example 1: Calculate the perimeter of square whose side is 8 cm.
Solution:length of one side a = 8 cm
The following is the formula to determine the perimeter of square:
The perimeter of Square = 4 × a units.
Replace the value of “a” in the formula for the perimeter,
Or, P= 4 ×8 cm
Or, P = 32 cm
The perimeter of square is 32 cm.

Example 2: Find the side of a square whose perimeter is 52 units.
Solution:
Given: The perimeter of the square = 52 units
Using the formula for the perimeter of the square,
The perimeter of Square = 4 × a units.
By substituting the perimeter value,

we obtain 52 = 4 × sides,

or, sides = 52/4 = 13 units.

Example 3: A square-shaped football field with a 10 m-long side. Find the perimeter of the ground.
Solution:

In the given problem. The length of one side of the ground  is 10 m

The formula for calculating the perimeter of a Square = 4 ×  length of a side,

Or,P = 4 × length of a side
Or,P =4 × 10 m
Or,P = 40 m

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