Perimeter Formulas for Geometric Shapes (original) (raw)

Last Updated : 6 Mar, 2026

Perimeter formulas are used to calculate the total length around any geometric shape. Geometry is all around us, from everyday objects to buildings, and understanding the perimeter is essential in many practical applications.

In mathematics, the study of shapes and their dimensions is called mensuration. It helps calculate the perimeter, area, and volume of shapes. The perimeter is the total boundary length of a closed figure, calculated by adding the lengths of its sides (e.g., triangle, rectangle, square, circle, etc.).

**Formula for Perimeter of Any Closed Figure = Sum of All Sides

Perimeter is used for solving various mathematical problems, and perimeter formulas of different shapes are added below.

**Perimeter of a Triangle

A triangle is a closed figure that is formed by three straight lines. These lines form sides of a triangle, so it has three sides, say A, B, and C. These three sides can be the same or different depending on the type of triangle.

There are three types of triangles:

**Scalene Triangle****:** The triangle in which all three sides are different is called the scalene triangle.

**Perimeter of Scalene Triangle = A + B + C

**Isosceles Triangle****:** The triangle in which two sides are equal is called the isosceles triangle.

Here two sides of the isosceles triangle are equal.

**Perimeter of Isosceles Triangle = A + A + B = 2(A)+B

**Equilateral Triangle****:** The triangle in which all three sides are equal is called an equilateral triangle.

Here all three sides are equal.

**Perimeter of Equilateral Triangle = A + A + A = 3A

**Perimeter of a Square

A square is a closed figure that is made of four straight lines. All four lines are equal, and all four angles of a square are 90 degrees.

**Perimeter of Square = Sum of all 4 sides = 4A

**Perimeter of Rectangle

A rectangle is a closed figure that is made of four straight lines. Both pairs of opposite lines are equal, and all four angles of a rectangle are 90 degrees.

**Perimeter of Rectangle = Sum of all sides = 2 × A + 2 × B = 2(A + B)

**Perimeter (or Circumference) of Circle

A circle is a closed figure whose boundary is at a constant distance from the center of the circle. This constant distance from the center of the circle to the boundary is called the radius of the circle.

For a circle with a radius R

**Circumference of Circle = 2πR

Perimeter of a Parallelogram

A parallelogram is a quadrilateral with opposite sides parallel and equal. The rectangle is also considered a parallelogram. The perimeter of a parallelogram with length "l" and width "w" is,

**Perimeter of Parallelogram = 2(l + w) units

Perimeter of a Rhombus

A rhombus is a quadrilateral with all four sides equal and opposite sides parallel. For a Rhombus of sides, **of its perimeter is,

**Perimeter of Rhombus = 4a units

Perimeter of a Kite

A kite is a quadrilateral in which the pairs of adjacent sides are equal. Suppose the two sides of a kite are a and b units; then its area is,

**Perimeter of Kite = 2(a + b) units

Perimeter of a Trapezoid

A trapezium/trapezoid is a quadrilateral with one pair of opposite sides parallel. If all four sides of the trapezium are, a, b, c, and d then the perimeter of the trapezium is,

**Perimeter of Trapezoid = a + b + c + d units

Perimeter of a Regular Polygon

A regular polygon is a polygon in which all the sides are equal. Suppose we have an 'n'-sided polygon with a length of each side 'a'; then its perimeter is calculated as,

**Perimeter of Regular Polygon = n.a units.

Perimeter of an Irregular Polygon

An irregular polygon is a polygon in which all the sides of the polygon are unequal. Suppose we have an 'n'-sided polygon with the lengths of sides being a, b, c, d,...; then its perimeter is calculated as,

**Perimeter of Irregular Polygon = (a + b + c + d + ....) units.,

Solved Examples of **Perimeter Formulas

**Example 1: Find the perimeter of a triangle that has sides a = 5 cm, b = 8 cm, c = 10 cm.
**Solution:

Perimeter of Scalene Triangle(P) = Sum of All Sides
Perimeter(P) = a + b + c
P = 5 + 8 + 10

Perimeter(P) = 23 cm

**Example 2: Find the Circumference of a circle whose radius is 7 cm.
**Solution:

Perimeter/Circumference of Circle(C) = 2 × π × R
C = 2 × (22/7) × 7, we know: ****(π = 22/7)**

C = 44 cm

**Example 3: Find the perimeter of the square with the side 10 cm.
**Solution:

Perimeter of a Square = Sum of All Sides
Perimeter(P) = 4 × Side
P = 4 × 10
P = 40 cm

**Example 4: Find the perimeter of a **rectangle whose length (l) = 5 cm and breadth (b) = 8 cm.
**Solution:

Perimeter of Rectangle(P) = 2 × (l + b)
P = 2 × (5 + 8)
P = 2 × (13) = 26 cm

**Example 5: Find the perimeter of an equilateral triangle whose side is 8 cm
**Solution:

Given,
Side of Equilateral Triangle = 8 cm
Perimeter of Equilateral Triangle(P) = 3 × (Side)
P = 3 × 8 = 24 cm

Practice Problem Based on Perimeter Formulas for Geometric Shapes

**Question 1. The sides of an irregular pentagon are 5 cm, 7 cm, 10 cm, 6 cm, and 8 cm. Find the perimeter.

**Question 2. A regular hexagon has sides of length 8 meters. What is its perimeter?

**Question 3. A trapezoid has sides of length 5 cm, 10 cm, 7 cm, and 12 cm. Find the perimeter.

**Question 4. A kite has adjacent sides of lengths 10 cm and 14 cm. What is the perimeter?

**Question 5. A rhombus has sides of length 8 cm. What is its perimeter?

**Question 6. A circle has a radius of 5 cm. Calculate its circumference.

**Answer:-

1. 36 cm.
2. 48 cm.
3. 34 cm.
4. 48 cm.
5. 32 cm.
6. 31.4 cm.