# ✅ Formula for calculating the perimeter of a square ⭐️⭐️⭐️⭐️⭐

5/5 - (1 vote)

## 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.

## 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

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.

### Tricky math problems with the squares:

Type I: Finding side length when only the perimeter is given.

Example 1. If the perimeter of the given square is 12 cm. What will be the length of its side?

Solution: Given, the perimeter of the square is 12 cm.

Let the side length be ‘a’ cm.

We know that, the perimeter of a square = 4 × (side length)

12=4×(a)

a = 3 cm

Type II: Finding sides using square properties.

Example 2.If a = 4 cm in the given square. Find b, c. and d.

Solution: Given that side a = 4 cm.

To find side b, c, and d  we use the property of the square which states that all the sides of a square are equal.

Therefore, a = b = c = d = 4 cm

Type III: Finding perimeter when one of the sides is given.

Example 3. One of the sides of a square is 5 cm. What will be its perimeter?

Solution: Given, one side of the square is 5 cm.

We know that, the perimeter of a square = 4 × (side length)

= 4×(5)

= 20 cm

Example 4. The length of a side of the square wooden frame is 5 cm. Find the total length of the wood used in the frame.

Solution: Given, the length of a side of this wooden frame is 5 cm.

As we know, the perimeter of a square = 4× (side length)

= 4  (5)

= 20 cm

Hence, the total length of the wood used is 20 cm.

Properties of square:
·  Diagonals of a square (quadrangle) bisect each other
·  Diagonals of a square (quadrangle) bisect its angles.
·  Diagonals of a square (quadrangle) are perpendicular.
·  Opposite sides of a square (quadrangle) are both parallel and equal.
·  All four angles of a square (quadrangle) are equal. (Square is 360/4 = 90 degrees, so every angle of a square (quadrangle) is a right angle.)
·  The diagonals of a square (quadrangle) are equal.