# How to find the perimeter of an octagon – Python Program to Compute the Area and Perimeter of Octagon

How to find the perimeter of an octagon: In the previous article, we have discussed Python Program to Compute the Area and Perimeter of Heptagon
Math Module :

How to find the perimeter of a octagon: Python’s math module is a built-in module. By importing this module, we can perform mathematical computations.

Numerous mathematical operations like ceil( ),floor( ),factorial( ),mod( ),value of pi ,…..etc .can be computed with the help of math module.

Octagon:

Perimeter of octagon formula: An octagon is a polygon with eight sides. It has eight different angles.

Octagon = octa + gon, where octa is the number eight and gon is the number of sides.

In an octagon, there are 20 diagonals.

Formula to calculate the area of an Octagon:

A = 2(1+⎷2)a²
In which  a is the Octagon’s side length
Formula to calculate the perimeter of a Octagon:
perimeter = 8a
Given the Octagon’s side length and the task is to calculate the area and perimeter of the given Octagon.
Examples:

Example1:

Input:

Given The Octagon's side length = 6

Output:

The Octagon's Area with given side length { 6 } = 173.82337649086284
The Octagon's Perimeter with the given side length { 6 } = 48

Example2:

Input:

Given The Octagon's side length = 12.5

Output:

The Octagon's Area with given side length { 12.5 } = 754.4417382415921
The Octagon's Perimeter with the given side length { 12.5 } = 100.0

## Program to Compute the Area and Perimeter of Octagon

Perimeter of a octagon: Below are the ways to Calculate the area and perimeter of a heptagon with the given Octagon’s side length:

### Method #1: Using Mathematical Formula (Static Input)

Approach:

• Import the math module using the import keyword.
• Give the Octagon’s side length as static input and store it in a variable.
• Calculate the area of the given Octagon using the above given mathematical formula and sqrt(), math.pow() functions.
• Store it in another variable.
• Calculate the perimeter of the given Octagon using the above given mathematical formula.
• Store it in another variable.
• Print the Octagon’s area with the given side length.
• Print the Octagon’s perimeter with the given side length.
• The Exit of the program.

Below is the implementation:

# Import the math module using the import keyword.
import math
# Give the Octagon's side length as static input and store it in a variable.
side_len = 6
# Calculate the area of the given Octagon using the above given mathematical formula
# and sqrt(), math.pow() functions.
# Store it in another variable.
octgn_area = (2*(1+math.sqrt(2))*math.pow(side_len, 2))
# Calculate the perimeter of the given Octagon using the above given mathematical formula.
# Store it in another variable.
octgn_perimetr = (8*side_len)
# Print the Octagon's area with the given side length.
print(
"The Octagon's Area with given side length {", side_len, "} =", octgn_area)
# Print the Octagon's perimeter with the given side length.
print(
"The Octagon's Perimeter with the given side length {", side_len, "} =", octgn_perimetr)


Output:

The Octagon's Area with given side length { 6 } = 173.82337649086284
The Octagon's Perimeter with the given side length { 6 } = 48

### Method #2: Using Mathematical Formula (User Input)

Approach:

• Import the math module using the import keyword.
• Give the Octagon’s side length as user input using float(input()) function and store it in a variable.
• Calculate the area of the given Octagon using the above given mathematical formula and sqrt(), math.pow() functions.
• Store it in another variable.
• Calculate the perimeter of the given Octagon using the above given mathematical formula.
• Store it in another variable.
• Print the Octagon’s area with the given side length.
• Print the Octagon’s perimeter with the given side length.
• The Exit of the program.

Below is the implementation:

# Import the math module using the import keyword.
import math
# Give the Octagon's side length as user input using float(input()) function and
# store it in a variable.
side_len = float(input("Enter some random number = "))
# Calculate the area of the given Octagon using the above given mathematical formula
# and sqrt(), math.pow() functions.
# Store it in another variable.
octgn_area = (2*(1+math.sqrt(2))*math.pow(side_len, 2))
# Calculate the perimeter of the given Octagon using the above given mathematical formula.
# Store it in another variable.
octgn_perimetr = (8*side_len)
# Print the Octagon's area with the given side length.
print(
"The Octagon's Area with given side length {", side_len, "} =", octgn_area)
# Print the Octagon's perimeter with the given side length.
print(
"The Octagon's Perimeter with the given side length {", side_len, "} =", octgn_perimetr)


Output:

Enter some random number = 12.5
The Octagon's Area with given side length { 12.5 } = 754.4417382415921
The Octagon's Perimeter with the given side length { 12.5 } = 100.0

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