### Perimeter of a Square

# Definition Perimeter of a square

**WHAT IS A PERIMETER?**

The length of the boundary or sides of any two-dimensional shape is called the perimeter. For polygons, perimeter can be calculated by adding the distances as you move around the shape.

**WHAT IS A SQUARE?**

A square is a plane closed figure with all the four sides equal and four right (90°) angles. A square has two diagonals that are equal. The diagonals of the square bisect each other at 90°. The diagonal of the square divide it into two isosceles right-angled triangles.

**NOTE**: 1. The diagonal of the square is greater than the sides of the square.

- Perimeter of a regular polygon = Number of sides × Length of one side.
- In circle, The distance around a circle is known as its circumference.
- If a wire in the shape of a square is rebent into a rectangle, then the area of both the shapes remains the same, but perimeter may vary.

**PERIMETER OF A SQUARE**

The **perimeter **of a square is the total length of the four equal sides of the square.

**FORMULA OF PERIMETER OF A SQUARE **

** **= Sum of all the sides

= side + side + side + side

As we know, length of all the sides of a square is equal.

So, Perimeter(P) = 4 x side

Let the side of the square be a units

So, Perimeter of square = a + a + a + a

= 4 x a

= 4 x side

So, Perimeter of square = 4 x side

**UNIT OF PERIMETER OF SQUARE:**

The unit to determine the value of the square of the perimeter can be millimetre (mm), centimetre (cm), metre (m), etc.

**METHODS OF FINDING THE PERIMETER OF SQUARE**

**Using the Formula of Perimeter of a Square**

The perimeter of the square can also be calculated by adding the value of all the four sides of a square.

From the formula of Perimeter of a square,

P = 4 x side

We can find the perimeter of a square.

**Perimeter of Square using Diagonal**

The perimeter of the square can also be calculated if the length of its diagonal is known.

From the Pythagorean theorem, we know that the side of a square is equal to the diagonal divided by the square root of 2.

So, Side = Diagonal/√2

Then, Side = √2(Diagonal/2)

And Perimeter of square = 4 x side

= 4 x √2(Diagonal/2)

= 2√2 (Diagonal)

Perimeter of square = 2√2(Diagonal) units.

**Perimeter of Square using Area**

The area of a square is the space occupied by the square.

The formula for area of square is given by:

Area of a square = side × side = side² sq. units

where “s” is the length of one side.

Now, we can write, side of the square as,

side = √Area

Hence, the perimeter of square will be:

Perimeter = 4 x side

So, Perimeter of square = 4 x √Area units.

**DIFFERENCE BETWEEN AREA AND PERIMETER**

**Area: **The area is the space occupied or enclosed by a closed shape. The area of the square is obtained by the product of the length of any two sides of a square. The unit of area is in square units like sq.cm, sq. m, sq. km etc.

**Perimeter:** The perimeter is the total distance along the boundary of a closed figure. The perimeter of the square is obtained by adding all the sides of a square. The unit of the perimeter is in cm, mm, m, km etc.

### Videos (3)

### Examples

## Q1 .Calculate the perimeter of a square with each side is of length 4cm.

## Solution:

Given: Side of a square is 4cm

We know that, Perimeter of a square = 4 x side

= 4 x 4 = 16cm.

Therefore, the perimeter of square = 16cm.

## Q2. If the perimeter of a square is 96 cm, find its side

## Solution:

Given: Perimeter of a square is 96cm

We know that, Perimeter of a square = 4 x side

or, Side of a square = Perimeter of a square/4

= 96/4

= 24cm.

So, the side of square is 24cm.

## Q3.The square has side of length 200 cm. Find its perimeter in meter.

## Solution:

Side of a square is 200cm

And, Perimeter of a square = 4 x side

= 4 x 200

= 800cm

We know that, 1m = 100cm or 100cm = 1m

So, 800 cm = 800/100m

= 8m

So, Perimeter of the square is 8m.

## Q4.If area of square is 81 sq.cm. Find its perimeter. SOLUTION: We know that,

## Solution:

Perimeter of square = 4√Area

= 4√81

= 4 x 9

= 36cm.

## Q5.Ram takes four rounds of a square park of side 45m. Find the distance travelled by Ram.

## Solution:

Side of the square park is 45m.

We know, the perimeter of a square = 4 x side

= 4 x 45 metres

= 180 metres.

Therefore, the boundary of the square park measures 180 metres.

If Ram takes four rounds of the park, then the total distance travelled by Ram

= 4 x 180 metres

= 720 metres.

## Q6.What is the Perimeter of a square and also find the cost of fencing a square park of side 100 metres at the rate of Rs 10 per metre.

## Solution:

To find the cost of fencing a square park, we have to find out the length of the boundary or the perimeter of a square park.

We know that,

The perimeter of a square = 4 x side

If the side of the square park is 100 metres,

So, the perimeter of a square = 4 x 100

= 400 metres.

The cost of fencing 1 metre is Rs 10

So, the cost of fencing 400 metres will be 400 x 10 =Rs. 4,000.

Therefore, the cost of fencing a square park of sides 100 metres is Rs 4,000.

## Q7.The measurements of a square and a rectangular field with the same perimeter is given. Which has the larger area?

## Solution:

Let the breadth of the rectangle be x.

Given: The perimeter of the rectangle is equal to the perimeter of the square.

Perimeter of rectangle = 2(l + b)

Perimeter of square = 4 x side

Therefore, 2(80+x) = 4 × 60

80 + x = 240/2

80 + x = 120

x = 120 – 80 = 40

i.e., breadth of the rectangle = 40 m

Area of the square = Side x Side

= (60 × 60) m2

= 3600 m2

Area of the rectangle = length x breadth

= (40 × 80) m2

= 3200 m2

Hence, the square field is larger than the rectangular field.

### Practice Questions

## Perimeter of Square Practice Questions

### Related Study Materials

### FAQ

### What is the perimeter of a square?

Perimeter is the total distance around a closed figure.

### What is the formula of the perimeter of a square?

The formula for the perimeter of square is equal to 4 times the length of each side of square.

Perimeter = 4 x length of a side of the square.

### What is the unit of perimeter of a square?

The unit of perimeter of a square is in m, cm, mm etc.

### How to find the perimeter of the square?

Add all the sides of the square to find the perimeter of the square.

### What is the area of a square?

The number of square units that are required to fill the total amount of space bounded by the four equal sides of the square or it can be referred as the total amount of region enclosed in the four sides of a square.

Area of a square = Side x Side = (Side)2

### What is the unit of area of a square?

Unit of area of a square is in square units like cm2, m2, km2 etc.

### How to calculate the area of square when diagonal is given?

Area of a square using diagonals = Diagonal²/2

For example: The diagonal of a square is 8m.

Area = 82/2 = 64/2 = 32 units.

### If the side of a square is 7 m, then find the perimeter of the square.

Given: Side of a square = 7m

As we know that, Perimeter of a square = 4 x side

So, Perimeter of a square = 4 x 7 = 28m.

### Find the perimeter of a square whose area is 100 m². Solution:

Given: Area = 100 m²

Perimeter of square = 4√Area

= 4√100

= 4 x 10 = 40m.

Therefore, the perimeter of a square is 40m.

Acute Angled Triangle | Right Angled Triangle | Obtuse Angled Triangle |

### Videos(3)

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