Perimeter of Square

# Perimeter of Square

The perimeter of a square represents the entire length of its boundary in a two-dimensional plane. Precisely, The perimeter of a square refers to the total path encircling the shape. Therefore, for a closed geometric figure, like a square, the perimeter is found by adding up all its sides.

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Since a square has four equal sides, its perimeter equals the sum of these four sides. The formula for the perimeter of a square is derived by adding the lengths of all sides.

## What is the Perimeter of Square?

The perimeter of a closed geometrical figure is the total distance around it. The perimeter of the square is the sum of all four equal sides of the square. As we all know, all sides of a square are of equal length. Therefore, the formula for the perimeter of a square simplifies to 4 times the length of one side.

## Perimeter of Square Formula

As we all know, the formula for the perimeter of a square simplifies to 4 times the length of one side. Therefore,

The perimeter of the Square = 4 × Side of the square

Measurement units like meters (m), centimetres (cm), inches (in), feet (ft), etc., are used to measure this distance.

### Perimeter of Square : Example

Lets consider a square whose side is 3cm each, therefore the perimeter of this square equals to the 4 times of the side of that square.

⇒ The perimeter of the Square = 4 × Side of the square

⇒ The perimeter of the Square = 4 × 3 cm = 12 cm

### Perimeter of Square: Derivation

The derivation of the perimeter of a square formula is straightforward. The perimeter is the total length of all the sides of the square. Now, we apply the general formula for the perimeter of a polygon, which is the sum of all its sides, to a square.

Therefore,

The formula for the perimeter of a square, length of whose side is A cm, is given by:

The perimeter of the Square = side + side + side + side = A + A+ A + A

Simplifying, we get:

The perimeter of the Square = 4A

Therefore, the final formula for the perimeter of a square is = 4 × Side of the square

## How to Solve the Perimeter of Square

We have studied one of the most commonly used and easiest methods above. Other than that, we have two more methods to find the Perimeter of the Square. They are:

1. Perimeter by using Diagonal
2. Perimeter by using Area

Let’s revise the simplest formula to solve the perimeter of the square:

The perimeter of the Square = side + side + side + side = A + A+ A + A

Simplifying, we get:

The perimeter of the Square = 4A

Therefore, the final formula for the perimeter of a square is = 4 × Side of the square

Now lets have a look at another two formulas.

### Perimeter by using Diagonal

If the length of the diagonal, d, is given, you can find the perimeter, P, using the formula:

P = d

Once you have the perimeter, you can also find the length of one side, s using the formula:

s = P/4

### Perimeter by using Area

We know Area of Square = s2 (where s is the side of the square)

A=s2

A=s

Also, the perimeter of the square with side s is equal to 4 times the side, i.e.,

P=4s

s= P/4

P/4 = A

P = 4A

After finding the perimeter, you can determine the length of one side, s, using s = P/4.

## Perimeter of a Rectangle

The perimeter of a rectangle is the complete length covered by its sides or boundaries. As a rectangle has four sides, the perimeter is the sum of all four sides. The formula for calculating the perimeter P of a rectangle, where l is the length and w is the width, is given by:

P = 2l + 2w = 2(l+w)

This formula accounts for the fact that opposite sides of a rectangle are equal in length, and by adding all four sides, we obtain the total perimeter of the rectangle.

## Perimeter of a Rectangle Formula

The derivation of the perimeter P of a rectangle is equal to the sum of all its four sides. Let’s denote the length of the rectangle as l and the width as w. Since opposite sides of a rectangle are equal, the perimeter can be expressed as:

P = l + w + l + w

Simplifying this, we get:

P = 2l + 2w

P = 2(l + w)

Thus, the derived formula for the perimeter of a rectangle is:

P = 2l + 2w

### Perimeter of a Rectangle: Example

Lets consider a rectangle whose length is 5cm and width is 3cm each. Therefore, the perimeter of this rectangle equals to:

P = l + w + l + w

P = 2(l + w)

P = 2l + 2w

We know, l= 5cm and w= 3cm

Therefore, P = 2(5 + 3) = 2(8) = 16cm

## FAQs on Perimeter of Square

### How do I find the perimeter of a square if the length of one side is given?

To find the perimeter of a square when the length of one side, s is given, you can use the formula: Perimeter = 4s

### Can I find the perimeter of a square if only the diagonal is known?

Yes, you can find the perimeter P using the formula: P = root of diagonal

### Can the perimeter of a square be found if the area is provided?

Absolutely. If the area A of the square is given, you can find the perimeter using P = 4 root of A

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