Perimeter of Square | Formula, Derivation, Examples

A square is a four-sided polygon (quadrilateral) with the following properties.

• All sides are of equal length, and each angle is a right angle (90°).
• It is a type of rectangle where the length and width are the same.
• A square also has the property that its diagonals are equal in length and bisect each other at right angles.
• The perimeter of a square is 4 x a where a is length of a side.
• Square of area is a²

Visual Representation of a Perimeter of a Square

• Edges: The four equal sides of the square are highlighted, representing the boundaries.
• Diagonal: The diagonal of the square is shown, connecting opposite vertices.
• Angles: All four angles will be right angles (90°).
• Vertex: The corners of the square, where two edges meet, are labeled as vertices.
• Perimeter (Blue Color): The perimeter is illustrated in blue, emphasizing the total length of the boundary.
• Area (Green Color): The area of the square is shown in green, representing the space enclosed within the square.

Perimeter of Square Formula

The perimeter of the Square can be calculated using the following formula:

Perimeter of square = 4 × side

The unit for the perimeter of a square is the unit used for length. It is measured in meters (m), centimeters (cm), inches (in), etc.

Various Methods to Find Perimeter of Square

Perimeter of square can be calculated using these three methods:

• Using Side length
• Using Diagonal
• Using Area

The Perimeter of the the Square using Side Length

The below-given steps can be used to find the perimeter of square using side length,

Step 1: Measure the side of the square.
Step 2: Multiply the side length by 4.
Step 3: Express the perimeter obtained in the respective unit.

Perimeter of Square 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.

The of a square is given by the following formula :

The formula for the Perimeter of square using the diagonal is given below.

P = 4 × (Diagonal/√2).

Read More: Diagonal of the square.

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,

Related Reads:

• Perimeter of Rectangle
• Perimeter of Geometrical Shapes
• Quadrilateral
• Perimeter of Triangle
• Circumference of a Circle

Solved Examples on Perimeter of Square

Some Solved example problems on the Perimeter of a Square.

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