Perimeter of Square

Have you ever thought about what length of string you need to wrap a gift or how many meters you walked around a square park or how many marbles you need to for the boundary of your room?


Perimeter finds its application in various fields and in our day to day life. Suppose uncle John completes two rounds of a square park every morning. Now, to find out the perimeter of the square park to calculate how many kilometres uncle John covers every day. Similarly, a farmer needs to know the cost of fencing his field in order to save his crops from ruminant animals. To find the cost of fencing he needs to know the perimeter of his field.                        

What is Perimeter of a Square?

Any shape that can be laid on a flat surface is called a two-dimensional object. Square is one of the 2D-Shape having four equal sides and four corners of 90 degrees each. The length of the boundary or sides of any two-dimensional shape is called the perimeter. The perimeter of a Square is the sum of the length of all the four sides of a square.


The Perimeter of Square formula:

The perimeter of a square = Sum of all the Sides     (or)

                                                = Side+Side+Side+Side.


Now, as we know, the length of all the four sides of a square are equal so the perimeter is four times the length of any side of a square.

The perimeter of a square = 4 x sides.

Let’s take an example of a square having side ‘a’.

Perimeter  = side x side x side x side

                    = a x a x a x a

                    = 4 x a

                    = 4a


Solved examples

Below are the Perimeter of Square Formula examples:

Problem 1:

Preeti takes three rounds of a square park of side 70m. Find the distance travelled by Shaina.

Solution: Side of the square park is 70 metre.

We know, the perimeter of a square = sum of all the sides

                                   = 70 x 70 x 70 x 70 metres

                                   = 4 x 70 metres

                                   = 280 metres.

Therefore, the boundary of the square park measures 280 metres.

If Preeti takes three rounds of the park, then the total distance travelled by Preeti

= 3 x 280 metres

= 840 metres.


Problem 2: 

The lid of a square box of side 50cm is sealed with tape. What is the length of the tape?

Solution: 

Length of the side of the square box is 50cm. 

The length of the tape is equal to the perimeter of the box

The perimeter of the box = 4 x side

                                              = 4 x 50 cm

                                              = 200 cm.

Thus, the length of the tape is 200cm.


Problem 3:

If the perimeter of a square is 20m, then what is the side of the square?

Solution:

We know, 

Perimeter = 4 x side

Side = Perimeter / 4

        = 20 / 4 cm

        = 5 cm.


Problem 4: 

What is the Perimeter of a square and also find the cost of fencing a square park of side 250 metres at the rate of Rs 20 per metre.

Solution: To find the cost of fencing a square park we need to find out the length of the boundary of a square park.

The perimeter of a square = 4 x sides

 If the side of the square park is 250 metres then,

 The perimeter of a square = 4 x 250

                                                 = 1000 metres.

The cost of fencing 1 metre is Rs 20 

So, the cost of fencing 1000 metres will be 1000x20  i.e, 20,000.

Therefore the cost of fencing a square park of sides 250 metres is Rs 20,000.