Last modified on November 18th, 2021

chapter outline

 

Perimeter of Square

Perimeter of a square is the total length around the edge of the square. We can find the perimeter of a square by adding all its four sides. It is measured in units such as m, cm, in, and ft.

Formulas

Using Side Length

The basic formula to calculate the perimeter of a square is given below:

Perimeter of a Square

Derivation

As we know, perimeter of a square is the total length around the boundary of a square. Thus, we need to add all its four sides to find the perimeter.

Mathematically,

Perimeter (P) = sum of all sides

 = side + side + side + side

 = 4 × side

 = 4a, where a = side length

Let us solve some examples to understand the concept better.

Find the perimeter of a square with a side length of 9 m

Solution:

As we know,
Perimeter (P) = 4a, here a = 9 m
= (4 × 9) m
= 36 m

If the perimeter of a square is 92 units, find its side

Solution:

As we know,
Perimeter (P) = 4a, here P = 92 units
=> 92 = 4a
=> a = 92/4
=> a = 23 units

Using Diagonal

The formula to calculate the perimeter of a square when only diagonal is known is given below:

Perimeter of Square Using Diagonal

Derivation

Perimeter of Square Using Diagonal Derivation

In square ABCD,

Applying Pythagoras theorem, we get

d2 = a2 + a2

=> d2 = 2a2

=> d = a × √2

=> a = d/√2

Since, Perimeter (P) = 4 × side = 4a

 = 4 × d/√2

 = 4 × √2d ×/2

 = 2√2 × d

Hence,

Perimeter (P) = 2√2 × d

Let us solve an example to understand the concept better.

Find the perimeter of a square with a diagonal of 11 cm

Solution:

As we know,
Perimeter (P) = 2√2 × d, here d = 11 cm
 = (2√2 × 11) cm
 = 22√2 cm

Using Area

The formula to calculate the perimeter of a square when only the area is known is given below:

Perimeter of Square Using Area

Derivation

As we know,

Area (A) = (side)2 = a2

=> a = √A

Again, as we know

Perimeter (P) = 4a, here a = side

Perimeter (P) = 4 × √A

Let us solve an example to understand the concept better.

Calculate the perimeter of a square park with an area of 20 cm2.

Solution:

As we know,
Perimeter (P) = 4 × √A, here A = 20 cm2
 = (4 × √20) cm
 = 4√20 cm
Alternative Method
As we know,
Area (A) = a2, here A = 20 cm2
=> 20 = a2
=> a2 = 20
=> a = √20 cm
Now, as we know
 Perimeter (P) = 4a, here a = √20 cm
=> (4 × √20) cm
=> 4√20 cm

Last modified on November 18th, 2021

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