Perimeter of Polygon
The perimeter of a polygon is defined as the sum of lengths of the boundary of the polygon shape. In other words, we say that the total distance covered by the sides of any polygon gives its perimeter. In this lesson, we will learn to determine the perimeter of polygons whether regular or irregular polygons, and find the difference between the area and perimeter of the polygons in detail.
1.  What is the Perimeter of Polygon? 
2.  Difference Between Area and Perimeter of Polygon 
3.  Formula for Perimeter of Polygon 
4.  Perimeter of Polygons with Coordinates 
5.  FAQs on Perimeter of Polygons 
What is the Perimeter of Polygon?
The perimeter of a polygon is the measure of the total length of the boundary of the polygon. As polygons are closed plane shapes, thus, the perimeter of the polygons also lies in a twodimensional plane. The unit of the perimeter of any polygon is always given as (unit) where the word unit can be SI units (meters or centimeters, etc.) or USCS units (inches or feet, etc.).
Difference Between Area and Perimeter of Polygon
The area and perimeter of polygons can be measured if the lengths of the sides of the polygon are known. Before we differentiate between both of them, it is necessary to understand the basic difference between perimeter and area. Look at the table below to understand this difference better.
Criterion of Difference  Area of Polygon  Perimeter of Polygon 

Definition  The measurement of space enclosed by any polygon is known as its area.  The distance around a polygon that is obtained by adding the length of all its sides is known as its perimeter. 
Formula  The area of polygons can be determined using different formulas by checking whether the polygon is a regular polygon or not.  The perimeter of polygon = Length of Side 1 + Length of Side 2 + ...+ Length of side N (for an N sided polygon) 
Unit  (meters)^{2}, (centimeters)^{2}, (inches)^{2}, (feet)^{2}, etc.  meters, centimeters, inches, feet, etc. 
There is one similarity between the determination of area and perimeter of a polygon, both depend directly on the length of the sides of the shape and not directly on the interior angles or the exterior angles of the polygon.
Formula for Perimeter of Polygon
We can categorize a polygon as regular and irregular polygon based on the length of its sides. This differentiation brings a difference while we determine the value of the perimeter of polygons. The perimeter formula of some known polygons is given as:
 Perimeter of a triangle = a + b + c, where, a, b, and c are the length of its sides.
 Perimeter of a rectangle = 2 × (length + breadth)
Before we proceed to calculate the perimeter of the polygon, we first understand whether the given polygon is a regular polygon or an irregular polygon.
Perimeter of Regular Polygons
A polygon that is equilateral and equiangular is known as a regular polygon. Thus, we calculate the value of the perimeter of regular polygons using the formulas associated with each polygon. The formulas of some commonly used regular polygons are:
Names of Regular Polygon  Perimeter of Regular Polygon 

Equilateral Triangle  3 × (length of one side) 
Square  4 × (length of one side) 
Regular Pentagon  5 × (length of one side) 
Regular Hexagon  6 × (length of one side) 
In order to determine the perimeter of a regular polygon, if the number of its sides are known, is given by:
 The perimeter of regular polygon = (number of sides) × (length of one side)
Example: Find the perimeter of a regular hexagon whose each side is 6 inches long.
Solution: Given the length of one side = 6 inches and a number of sides = 6 (as it is a hexagon).
Thus, the perimeter of the regular hexagon = (number of sides) × (length of one side) = (6 × 6) = 36 inches.
Therefore, the area of the regular hexagon is 36 inches.
Perimeter of Irregular Polygons
Polygons that do not have equal sides and equal angles are referred to as irregular polygons. Thus, in order to calculate the perimeter of irregular polygons, we add the lengths of all sides of the polygon.
Example: Find the perimeter of the given polygon.
Solution: As we can see, the given polygon is an irregular polygon as the length of each side is different (AB = 7 units, BC = 8 units, CD = 3 units, and AD = 5 units)
Thus, the perimeter of the irregular polygon will be given as the sum of the lengths of all sides of its sides.
Thus, the perimeter of ABCD = AB + BC + CD + AD ⇒ Perimeter of ABCD = (7 + 8 + 3 + 5) units = 23 units
Therefore, the perimeter of ABCD is 23 units.
Area of Polygons with Coordinates
The area of polygons with coordinates can be found using the following steps:
 Step 1: Find the distance between all the points using the distance formula, D = \(\sqrt {\left( {x_2  x_1 } \right)^2 + \left( {y_2  y_1 } \right)^2 }\).
 Step 2: Once, the dimensions of the polygons are known find whether the given polygon is a regular polygon or not.
 Step 3: If the polygon is a regular polygon we use the formula, perimeter of regular polygon = (number of sides) × (length of one side) while if the polygon is an irregular polygon we just add the lengths of all sides of the polygon.
Example: What is the area of the polygon formed by the coordinates A(0,0), B(0, 3), C(3, 3), and D(3, 0)?
Solution: On plotting the coordinates A(0,0), B(0, 3), C(3, 3), and D(3, 0) on an XY plane and joining the dots we get,
It can be seen, the obtained figure shows a foursided polygon. In order to understand whether it is a regular polygon or not, we find the distance between all the points.
 Length of AB = \(\sqrt{({0  0})^2 + ({3  0})^2}\) = 3 units
 Length of BC = \(\sqrt{({3  0})^2 + ({3  3})^2}\) = 3 units
 Length of CD = \(\sqrt{({3  3})^2 + ({0  3})^2}\) = 3 units
 Length of DA = \(\sqrt{({0  3})^2 + ({0  0})^2}\) = 3 units
Now that we know the lengths of all sides of the given polygon is same, it shows, it is a square. Thus, the perimeter of the polygon ABCD is given as A = 4 × (length of one side) = 4 × (3) = 12 units.
Hence, the perimeter of the polygon with coordinates (0,0), (0, 3), (3, 3), and (3, 0) is 12 square units.
Perimeter of Polygons Examples

Example 1: Find the missing length of the polygon given in the image if the perimeter of the polygon is 18.5 units.
Solution: It can be seen that the given polygon is an irregular polygon. The perimeter of the given polygon is 18.5 units. The given lengths of the sides of polygon are AB = 3 units, BC = 4 units, CD = 6 units, DE = 2 units, EF = 1.5 units and FA = x units.
Given that, the perimeter of the polygon ABCDEF = 18.5 units
⇒ Perimeter of polygon ABCDEF = AB + BC + CD + DE + EF + FA = 18.5 units ⇒ (3 + 4 + 6 + 2 + 1.5 + x) units = 18.5 units. Thus, x = 18.5  (3 + 4 + 6 + 2 + 1.5) = 2 unitsTherefore, the missing length of polygon ABCDEF is 2 units.

Example 2: Determine the length of the side of the equilateral triangle, if its perimeter is 27 units.
Solution: Given, the perimeter of the polygon (equilateral triangle) = 27 units. Let the length of the side of the equilateral triangle is "a" units. Thus, the length of the side of the equilateral triangle is calculated as:
The perimeter of equilateral triangle = 3 × a
⇒ Perimeter of equilateral triangle = 3 × a = 27 units. Thus, a = 27/3 = 9 unitsTherefore, the length of the side of the equilateral triangle is 9 units.
FAQs on Perimeter of Polygons
What is the Perimeter of Polygon Definition?
The perimeter of a polygon is defined as the total length of the boundary of the polygon in a twodimensional plane. We can give the unit of the perimeter of the polygon using SI units or USCS units like meters or centimeters or inches or feet respectively.
How to Find Perimeter of a Polygon?
The perimeter of a polygon can be found by understanding whether there is a standard formula for the given polygon the calculation of its perimeter, it is a regular polygon, or is an irregular polygon. The steps to determine the perimeter of polygons are:
 Step 1: Find whether the given polygon is a regular polygon or not.
 Step 2: If it is a regular polygon or has a standard formula for the determination of the perimeter of the polygon, use it to determine the value with all the given dimensions of the polygon else the perimeter of the polygon can be determined by adding the lengths of all its sides.
 Step 3: Once the value of the perimeter of the polygon is obtained mention the unit that has to be placed with the value so obtained.
What is the Difference Between the Area and Perimeter of Polygons?
We obtain the perimeter of a polygon by summing the length of all its sides. The area of a polygon is determined by using the required formulas for the calculation of area or by reducing the polygon into smaller regular polygons. The unit of the area of a polygon is always given in (unit)^{2 }while the perimeter of a polygon is always given in units.
How Do You Find the Perimeter of Polygons with Vertices?
We determine the perimeter of polygons with vertices using the following steps:
 Step 1: First determine the distance between all the points using the distance formula, D = \(\sqrt {\left( {x_2  x_1 } \right)^2 + \left( {y_2  y_1 } \right)^2 }\).
 Step 2: Once the dimensions of the polygons are known, check if we can conclude whether the given polygon is a regular polygon or not.
 Step 3: The perimeter of the regular polygon can be found by using the formula, perimeter of regular polygon = (number of sides) × (length of one side) while if the polygon is an irregular polygon we add the lengths of all sides of the polygon.
How to Find the Perimeter of Regular Polygons?
The perimeter of a regular polygon can be found using the following steps:
 Step 1: Count the number of sides of the polygon.
 Step 2: Check the measurement of the length of one side.
 Step 3: Use the values obtained in Step 1 and Step 2 to determine the value of perimeter using the formula (number of sides) × (length of one side).
How to Find the Perimeter of Irregular Polygons?
In order to calculate the value of the perimeter of an irregular polygon we follow the below steps:
 Step 1: Find the measurement of each side of the given polygon (if not given).
 Step 2: Once the lengths of all sides are obtained, the perimeter is found by adding all the sides individually.
Is the Perimeter of Regular Polygon Directly Proportional to the Length of Side?
The perimeter of a regular polygon is given by the formula, Perimeter = (number of sides) × (length of one side). Thus, if the number of sides remains constant and the length of the side is increased, the value of the perimeter also increases. For example, a square having the length of one side of 4 units will have a larger perimeter as compared to a square having the length of one side of 2 units.
How Do You Find the Missing Side Length When the Perimeter of Polygon is Given?
We can find the missing side length when the perimeter of the polygon is given in the following way:
 Step 1: Find whether the given polygon is a regular polygon or not.
 Step 2: If the given polygon is a regular polygon, then we use the formula (number of sides) × (length of one side) to determine the missing side length. In case if the given polygon is an irregular polygon, then we add the lengths of all the sides and equate their sum to the given value of perimeter to obtain the missing side length.