Session 2: Perimeter of Square – Formula, Definition, Interactive and Examples

What is Perimeter?

Perimeter is the distance around a shape. In other words, the total boundary length of a closed two-dimensional figure is called its perimeter. To find the perimeter of any two-dimensional shape, find the sum of the lengths of all the sides.

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Perimeter of Square

A square is a plane figure whose all four sides are of equal lengths. The perimeter of the square is the total length of the boundary of a square. The perimeter of the square is the sum of all the sides of the square.

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Formula for Perimeter of Square

Consider a square shown below. Let s denote the length of each side.

[Figure 2]

It follows from this formula that

Side of a square=\(\frac{1}{4}\)Perimeter_square

Perimeter of Square – Examples

Example 1

Find the perimeter of a square with each side measuring 12 units.

We know,

Perimeter of a square =4×side

=4×12
=48 units

Example 2

If the perimeter of a square is 276 mm, find its side length.

We know,

Perimeter of a square =4×side.

∴ Side of the square=\(\frac{Perimete{{r}_{square}}}{4}\)                                

Example 3

A rope fence is to be put across a square boxing ring of side 24 feet. What length of the rope will be required if 1.8 feet are required for tying the knots?

The required length of rope is the same as the perimeter of the square boxing ring plus 1.8 feet for knots.

We have,

Perimeter of the square =4×side

=4×24
=96 feet

∴ The required length of the rope =96+1.8=97.8 feet.

Example 4

What is the cost of fencing a square farm whose each side is 45 m? The rate of fencing is ₹150 per metre.

We know,

Perimeter of a square =4×side

=4×45
=180 m

Cost of fencing 1 metre of the farm ₹=₹150.

∴ Cost of fencing 180 m of the farm₹=150×180=₹27000.

Example 5

The cost of constructing a boundary around a square garden at ₹960 per meter is ₹61440. Find the length of each side.

The total cost of constructing the wall = ₹61440.

Rate = ₹960/ m.

Cost = Perimeter × Rate

⇒ Perimeter =\(\frac{cost}{rate}\)

\(\frac{61440}{960}\)
=64 m

We know,

Perimeter of a square =4×side

 64=4×side

side=\(\frac{64}{4}\)

=16 m

Therefore, the length of each side of the square garden = 16 m.

Remember this!

• Perimeter is the total boundary length of a closed two-dimensional figure.
• The formula for perimeter of a square is: Perimeter_square=4×side
• Using the formula for perimeter of a square, we can find the side of the square: side=\(\frac{1}{4}\)Perimeter_square