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Perimeter Formulas for Geometric Shapes

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Perimeter Formulas are the mathematical Formulas used to calculate the total boundary length of any geometrical shape. In mathematics or in daily lives geometry and geometrical shapes always play an essential role. Starting from a simple tray to a big building, we are always surrounded by geometry in different shapes and sizes. The shape and surface to be taken up by such shapes need to be calculated so as to store them without any difficulty, or to meet the needs of the people using them. Such study or computation is given a special name in the field of mathematics.

Whenever the dimensions of various geometrical shapes are computed and their area or capacity is measured in mathematics, it is termed mensuration. Mensuration also helps to calculate the dimensions of other shapes from their surface area and capacity.

What is Perimeter?

Perimeter can be defined as the length of the boundary of any closed figure. Perimeter is the measure of all sides of any closed figure say a triangle, rectangle, square, circle etc.

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

Perimeter Formula of Different Shapes

Perimeter of different shapes is the sum of length of all the sides of the given shapes. Perimeter is used for solving various mathematical problems and perimeter formulas of different shapes are added below.

Perimeter of a Triangle

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

Types of Triangles

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

Perimeter of Scalene Triangle = A + B + C

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

Perimeter of 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.

Perimeter of Equilateral Triangle

Here all three sides are equal.

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

Perimeter of a Square

Square is a closed figure which is made by four straight lines. All four lines are equal and all four angles of a square are of 90 degrees.

Perimeter of Square

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

Perimeter of Rectangle

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

Perimeter of Rectangle

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

Perimeter (or Circumference) of Circle

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

Perimeter of Circle

For a circle with radius R

Circumference of Circle = 2Ï€R

Perimeter of a Parallelogram

Parallelogram is a quadrilateral with opposite sides parallel and equal. Rectangle is also considered a parallelogram. Perimeter of a parallelogram with length “l” and width “w” is,

Perimeter of Parallelogram = 2(l + w) units

Perimeter of a Rhombus

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

Perimeter of Rhombus = 4a units

Perimeter of a Kite

Kite is a quadrilateral in which the pair 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

Trapezoid is another name of trapezium. It is a quadrilateral with one pair of opposite sides parallel. If all four sides of trapezium are, a, b, c and d then the perimeter of 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 a ‘n’ sided polygon with 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 a ‘n’ sided polygon with length of sides to be a, b, c, d,… then its perimeter is calculated as,

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

Perimeter Formulas Table

Perimeter Formulas for various geometric shapes are added below in the table.

Perimeter of Geometric Shape

Perimeter Formula

Parameters

Perimeter of Triangle

(a + b + c)

a, b and c are sides of triangle

Perimeter of Parallelogram

2(L + W)

  • L is Length of Parallelogram
  • W is Width of Parallelogram

Perimeter of Square

4a

a is Side of Square

Perimeter of Rectangle

2(L + B)

  • L is Length of Parallelogram
  • W is Width of Parallelogram

Perimeter of Trapezoid

(a + b + c + d)

a, b, c and d are sides of triangle

Perimeter of Kite

2(a + b)

a is Length of First Pair

b is Length of Second Pair

Perimeter of Rhombus

4a

a is Side of Rhombus

Perimeter of Pentagon(Regular)

5a

a is Side of Pentagon

Perimeter of Hexagon(Regular)

6a

a is Side of Hexagon

Examples on Perimeter Formulas

Example 1: Find the perimeter of 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 perimeter of a circle whose radius is 7 cm

Solution:

Perimeter/Circumference of Circle(C) = 2×π×R

C = 2 × (22/7) × 7 (π = 22/7)

 C = 44 cm

Example 3: Find the perimeter of square which has each side equals to 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 Questions on Perimeter Formulas

Q1. Find the Perimeter of a Triangle with sides 10 cm, 11 cm and 12 cm.

Q2. Find the Perimeter of a Rectangle whose length and breadth are 12 cm and 16 cm respectively.

Q3. If the Perimeter of a square is 64 cm, find its side length.

Q4. Find the Perimeter of an Equilateral Triangle with side 12 cm.

Q5. Find the Perimeter of a Circle with Diameter 28 cm.

FAQs on Perimeter Formulas

1. What is the Perimeter of a Closed Shape?

Perimeter of closed shape is the sum of length of all the sides of the closed shape. It is also called the boundary of the closed shape.

2. What are the Units of Perimeter?

The perimeter is the sum of length all sides of a figure. Then its unit is the unit of length. The SI unit of Perimeter is ‘m’. The other units to measure perimeters are, cm, mm, inches, etc.

3. What is the Difference between Area and Perimeter?

Perimeter is the length of all the boundaries of the figure where as Area is the space occupied inside these boundaries of the figure.

4. What is the Perimeter of a Regular Polygon?

For a regular polygon with n sides and length of each side is “a” its perimeter is given using the formula, Perimeter of Regular Polygon = n×a units.

5. What is Perimeter Example?

Various examples of parameter are,

  • Perimeter of Square = 4a units
  • Perimeter of Rectangle = 2(l + b) units, etc.


Last Updated : 10 Jan, 2024
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