Perimeter of Square

The perimeter of a square is the total distance around its boundary.

• It is found by adding the lengths of all four sides.
• It is measured in meters (m), centimeters (cm), inches (in), etc.

Since all sides of a square are equal, the perimeter is equal to four times the length of one side of the square.

Various Methods to Find Perimeter

Perimeter of square can be calculated using these three methods:

1. Using Diagonal

If the side of the square is not given, but the diagonal is given, but the diagonal is given, then we make use of a different formula.

2. Perimeter of Square using Area

When the area of square is given, let us assume the Area of the the square is a. As we all know, Area, a = (side)²
Therefore, the perimeter of the square is,

P = 4\sqrt{a}

Solved Examples

Example 1: Find the perimeter of the square if the side given is 4 units. 
Solution:

The Perimeter of square is, P = 4 × side 
⇒ P = 4 × 4 
⇒ P = 16 units

Example 2: Find the perimeter if the area given is 25 sq units.
Solution:

Perimeter = 4√Area 
⇒ Perimeter = 4√25 
⇒ Perimeter = 20 units

Example 3: Find the diagonal if the perimeter of the square is 3√2 cm.
Solution:

Perimeter = 4 × (diagonal/√2) 
⇒ (3√2 × √2 ) /4 = diagonal
⇒ Diagonal = 1.5 cm

Example 4: Find the side and perimeter of the square if the diagonal given is 2√2 cm.
Solution:

Side = Diagonal/√2 
⇒ Side = 2√2/√2 
⇒ Side = 2 cm

Perimeter of square = 4×side 
⇒ Perimeter = 8 cm