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Program for Surface area of Dodecahedron
  • Difficulty Level : Hard
  • Last Updated : 23 Apr, 2018

Given the edge of the dodecahedron calculate its surface area. Surface area is the amount of space that all the faces of the shape takes up.

Formula: \mathbf{A=3\sqrt{25+10\sqrt{5}}\hspace{2 mm} a^{2}}
Examples:

Input : 3
Output : 185.812

Input : 7
Output : 1011.64

A dodecahedron is a 3-dimensional figure made up of 12 faces, or flat sides. All of the faces are pentagons of the same size.The word ‘dodecahedron’ comes from the Greek words dodeca (‘twelve’) and hedron (‘faces’). Every shape has properties and characteristics.So has dodecahedron

  • 12 equal pentagonal faces
  • 20 vertices
  • 30 edges

where pentagon is a 2-dimensional shape with 5 straight sides and 5 vertices. So, a dodecahedron has 12 of these flat, equal pentagonal faces.So one can think dodecahedron as a 12 faced dice(Usually not seen) but can be in a Battleball board game.

C++




// CPP program to calculate
// surface area of dodecahedron
#include <bits/stdc++.h>
using namespace std;
  
// utility Function
double area_of_dodecahedron(int side)
{
    return ((3 * sqrt(25 + 10 * (sqrt(5))))
                        * (pow(side, 2))) ;
}
  
// Driver Function
int main()
{
    int side = 3;
      
    cout<< "Surface area of dodecahedron = "
            << area_of_dodecahedron(side);
          
        return 0;
}


Java




//Java program to calculate
// surface area of dodecahedron
  
class GFG
{
  
    // Utility Function
    static double area_of_dodecahedron(int side)
    {
        return ((3 * Math.sqrt(25 + 10 * (Math.sqrt(5))))
                        * (Math.pow(side, 2))) ;
    }
      
    // Driver Function
    public static void main (String[] args)
    {
        int side = 3;
        System.out.println("Surface area of dodecahedron =" 
                              + area_of_dodecahedron(side));
    }
  
}
  
// This code is contributed by Azkia Anam.


Python3




# Python program to calculate
# surface area of dodecahedron
import math
  
# utility Function
def area_of_dodecahedron(side):
  
    return ((3 * math.sqrt(25 + 10 * (math.sqrt(5))))* (math.pow(side, 2)))
  
# Driver Function
side = 3
print("Surface area of dodecahedron = ",
      round(area_of_dodecahedron(side), 3))
  
# This code is contributed
# by Azkia Anam.


C#




//C# program to calculate
// surface area of dodecahedron
using System;
  
class GFG
{
  
    // Utility Function
    static float area_of_dodecahedron(int side)
    {
        return (float)((3 * Math.Sqrt(25 + 10 * (Math.Sqrt(5))))
                        * (Math.Pow(side, 2))) ;
    }
      
    // Driver Function
    public static void Main ()
    {
        int side = 3;
        Console.WriteLine("Surface area of dodecahedron ="
                            + area_of_dodecahedron(side));
    }
  
}
  
// This code is contributed by vt_m.


PHP




<?php
// PHP program to calculate
// surface area of dodecahedron
  
// utility Function
function area_of_dodecahedron( $side)
{
    return ((3 * sqrt(25 + 10 * (sqrt(5))))
                         * (pow($side, 2))) ;
}
  
// Driver Code
$side = 3;
  
echo("Surface area of dodecahedron = ");
echo(area_of_dodecahedron($side));
  
// This code is contributed by vt_m.
?>



Output:

Surface area of dodecahedron = 185.812



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