# What is the surface area of a octahedron – Python Program for Volume and Surface Area of Octahedron

What is the surface area of a octahedron: In the previous article, we have discussed Python Program for Volume and Surface Area of Frustum of Cone
Given the side of an octahedron and the task is to calculate the volume and surface area of an octahedron for the given side in python.

Octahedron :

Surface area of octahedron: A regular octahedron has eight faces, all of which are equilateral triangles. An octahedron’s area is equal to 2 multiplied by the length of an edge squared multiplied by the square root of three.

Formulas:

Surface Area of an Octahedron = 2*(sqrt(3))*(side*side)

The volume of an Octahedron = √2/3 × side3

Examples:

Example1:

Input:

Given side = 5

Output:

The Surface Area of an octahedron for the given side { 5 } =  86.60254037844386
The volume of an Octahedron for the given side { 5 } =  58.92556509887897

Example2:

Input:

Given side = 10

Output:

The Surface Area of an octahedron for the given side { 10 } =  346.41016151377545
The volume of an Octahedron for the given side { 10 } =  471.40452079103176

## Program for Volume and Surface Area of Octahedron in Python

Surface area of an octahedron: Below are the ways to calculate the volume and surface area of an octahedron for the given side in python:

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

Approach:

• Import math module using the import keyword.
• Give the side as static input and store it in a variable.
• Calculate the surface area of an octahedron using the above given mathematical formula and math.sqrt() function.
• Store it in another variable.
• Calculate the volume of an octahedron using the above given mathematical formula and math.sqrt() function.
• Store it in another variable.
• Print the surface area of a given octahedron.
• Print the volume of a given octahedron.
• The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the side as static input and store it in a variable.
gvn_side = 5
# Calculate the surface area of an octahedron using the above given mathematical
# formula and math.sqrt() function.
# Store it in another variable.
surfce_area = (2*(math.sqrt(3))*(gvn_side*gvn_side))
# Calculate the volume of an octahedron using the above given mathematical formula
# and math.sqrt() function.
# Store it in another variable.
rslt_volum = ((gvn_side*gvn_side*gvn_side)*(math.sqrt(2)/3))
# Print the surface area of a given octahedron.
print(
"The Surface Area of an octahedron for the given side {", gvn_side, "} = ", surfce_area)
# Print the volume of a given octahedron.
print(
"The volume of an Octahedron for the given side {", gvn_side, "} = ", rslt_volum)

#include <iostream>
#include<math.h>

using namespace std;

int main() {
double gvn_side = 5;
double surfce_area = ( 2 * ( sqrt ( 3 ) ) * ( gvn_side * gvn_side ) );
double rslt_volum = ( ( gvn_side * gvn_side * gvn_side ) * ( sqrt ( 2 ) / 3 ) );
cout << "The Surface Area of an octahedron for the given side {" << gvn_side << "} = " << surfce_area << endl;
cout << "The volume of an Octahedron for the given side {" << gvn_side << "} = " << rslt_volum << endl;

}

Output:

The Surface Area of an octahedron for the given side { 5 } =  86.60254037844386
The volume of an Octahedron for the given side { 5 } =  58.92556509887897

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

Approach:

• Import math module using the import keyword.
• Give the side as user input using the int(input()) function and store it in a variable.
• Calculate the surface area of an octahedron using the above given mathematical formula and math.sqrt() function.
• Store it in another variable.
• Calculate the volume of an octahedron using the above given mathematical formula and math.sqrt() function.
• Store it in another variable.
• Print the surface area of a given octahedron.
• Print the volume of a given octahedron.
• The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the side as user input using the int(input()) function and store it in a variable.
gvn_side = int(input("Enter some random number = "))
# Calculate the surface area of an octahedron using the above given mathematical
# formula and math.sqrt() function.
# Store it in another variable.
surfce_area = (2*(math.sqrt(3))*(gvn_side*gvn_side))
# Calculate the volume of an octahedron using the above given mathematical formula
# and math.sqrt() function.
# Store it in another variable.
rslt_volum = ((gvn_side*gvn_side*gvn_side)*(math.sqrt(2)/3))
# Print the surface area of a given octahedron.
print(
"The Surface Area of an octahedron for the given side {", gvn_side, "} = ", surfce_area)
# Print the volume of a given octahedron.
print(
"The volume of an Octahedron for the given side {", gvn_side, "} = ", rslt_volum)


Output:

Enter some random number = 10
The Surface Area of an octahedron for the given side { 10 } = 346.41016151377545
The volume of an Octahedron for the given side { 10 } = 471.40452079103176