Program to find the Area and Volume of Icosahedron

Given the side of an Icosahedron. The task is to find the area and volume of the given Icosahedron.

Examples :

Input : a = 5
Output : Area: 216.506
         Volume: 272.712

Input : a = 10
Output : Area: 866.0254
         Volume: 2181.695

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

In geometry, an Icosahedron is a regular polyhedron which contains 20 identical equilateral triangular faces, 30 sides, and 12 vertices.

Area of Icosahedron

Formula to find Area and Volume of Icosahedron: Let a be the side of Icosahedron, then

Surface area of Icosahedron = $5\sqrt{3} a^{2}$

and, Volume of Icosahedron = $\frac{5}{12}\left ( 3 + \sqrt{5} \right )a^{3}$

C++

// C++ program to find the Area and 
// volume of Icosahedron 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find area of Icosahedron 
float findArea(float a) 
{ 
    float area; 
  
    // Formula to calculating area 
    area = 5 * sqrt(3) * a * a; 
      
    return area; 
} 
  
// Function to find volume of Icosahedron 
float findVolume(float a) 
{ 
    float volume; 
  
    // Formula to calculating volume 
    volume = ((float)5 / 12) * (3 + sqrt(5)) * a * a * a; 
      
    return volume; 
} 
  
// Driver Code 
int main() 
{ 
    float a = 5; 
  
    // Function call to find area of Icosahedron. 
    cout << "Area: " << findArea(a) << endl; 
      
    // Function call to find volume of Icosahedron. 
    cout << "Volume: " << findVolume(a); 
  
    return 0; 
} 

Java

// Java program to find the Area and 
// volume of Icosahedron 
import java.io.*; 
  
class GFG { 
      
    // Function to find area of Icosahedron 
    static float findArea(float a) 
    { 
        float area; 
      
        // Formula to calculating area 
        area = (float)(5 * Math.sqrt(3) * a * a); 
          
        return area; 
    } 
      
    // Function to find volume of Icosahedron 
    static float findVolume(float a) 
    { 
        float volume; 
      
        // Formula to calculating volume 
        volume = (float)(((float)5 / 12) * (3 + Math.sqrt(5)) * a * a * a); 
          
        return volume; 
    } 
      
    // Driver code 
    public static void main (String[] args) 
    { 
        float a = 5; 
  
        // Function call to find area of Icosahedron. 
        System.out.println("Area: " + findArea(a)); 
          
        // Function call to find volume of Icosahedron. 
        System.out.println("Volume: " + findVolume(a)); 
    } 
} 

Python3

# Python3 program to  
# find the Area and 
# volume of Icosahedron 
  
# import math module  
# to use sqrt function 
from math import sqrt 
  
# Function to find  
# area of Icosahedron 
def findArea(a): 
  
    # Formula to calculate area 
    area = 5 * sqrt(3) * a * a 
    return area 
  
# Function to find  
# volume of Icosahedron 
def findVolume(a): 
      
    # Formula to calculate volume 
    volume = ((5 / 12) * 
              (3 + sqrt(5)) * 
               a * a * a) 
    return volume 
  
# Driver Code 
a = 5
  
# Function call to  
# find area of Icosahedron. 
print("Area: " , findArea(a)) 
      
# Function call to find 
# volume of Icosahedron. 
print("Volume: " , findVolume(a)) 
  
# This code is contributed 
# by ihritik 

C#

// C# program to find the Area and 
// volume of Icosahedron 
using System; 
  
public class GFG { 
      
    // Function to find area of Icosahedron 
    static float findArea(float a) 
    { 
        float area; 
      
        // Formula to calculating area 
        area = (float)(5 * Math.Sqrt(3) * a * a); 
          
        return area; 
    } 
      
    // Function to find volume of Icosahedron 
    static float findVolume(float a) 
    { 
        float volume; 
      
        // Formula to calculating volume 
        volume = (float)(((float)5 / 12) * (3 + Math.Sqrt(5)) * a * a * a); 
          
        return volume; 
    } 
      
    // Driver code 
    static public void Main () 
    { 
        float a = 5; 
  
        // Function call to find area of Icosahedron. 
        Console.WriteLine("Area: " + findArea(a)); 
          
        // Function call to find volume of Icosahedron. 
        Console.WriteLine("Volume: " + findVolume(a)); 
        //Code 
    } 
} 

PHP

<?php 
// PHP program to find  
// the Area and volume  
// of Icosahedron 
  
// Function to find area 
// of Icosahedron 
function findArea($a) 
{ 
    $area; 
  
    // Formula to  
    // calculating area 
    $area = 5 * sqrt(3) *  
                $a * $a; 
      
    return $area; 
} 
  
// Function to find  
// volume of Icosahedron 
function findVolume($a) 
{ 
    $volume; 
  
    // Formula to  
    // calculating volume 
    $volume = ((float)5 / 12) *  
                (3 + sqrt(5)) *  
                  $a * $a * $a; 
      
    return $volume; 
} 
  
// Driver Code 
$a = 5; 
  
// Function call to find  
// area of Icosahedron. 
echo "Area: " , findArea($a), "\n"; 
  
// Function call to find  
// volume of Icosahedron. 
echo "Volume: " , findVolume($a); 
  
// This code is contributed  
// by jit_t 
?> 

Output:

Area: 216.506
Volume: 272.712

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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