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 kilometers 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 the 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 traveled by Shaina.

Solution: Side of the square park is 70 meter.

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

                                   = 70 x 70 x 70 x 70 meters

                                   = 4 x 70 meters

                                   = 280 meters.

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

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

= 3 x 280 meters

= 840 meters.

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 250 meters at the rate of Rs 20 per meter.

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 meters then,

 The perimeter of a square = 4 x 250

                                                 = 1000 meters.

The cost of fencing 1 meter is Rs 20 

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

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

Finding the Perimeter of the Square using its Area 

Suppose the question does not specify the side length of the square. Instead, it gives you the area of the square and asks you to find the perimeter. 

Then, you can find the perimeter of the square by using the formula of the area of a square. Follow the steps mentioned below to understand how to determine the perimeter,

1. Read the question carefully and note down the area of the square. 

2. You can use the area to find the side length of the square. Here’s how: 

Area of square (A)= Side × Side 

So, Side = √A

3. Once you have obtained the side length, you can put its value in the formula of the perimeter of the square. 

Perimeter = 4 × √area 

Finding the Area of Perimeter using its Diagonals 

Like the above question, some questions will only specify the diagonal length of the square instead of the side length. In such cases, you can follow the steps mentioned below to find the perimeter of the square.

1. Go through the question thoroughly and note down the diagonal length. 

2. Use the diagonal length to find the side length of the square using the formula: 

Side = diagonal/√2 

3. Then apply the length of the side, obtained in the above step, in the formula of the perimeter of the square. You will get, 

Perimeter = 4 × diagonal/√2 

This way, you can find the perimeter of the square using only the length of the diagonals. By learning these formulas, you will be able to solve any question, based on the perimeter of a square, asked in your math exam.