# 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.

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

Surface area of Icosahedron =

and, Volume of Icosahedron =

## C++

 `// C++ program to find the Area and ` `// volume of Icosahedron ` `#include ` `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

 ` `

Output:

```Area: 216.506
Volume: 272.712
```

This article is attributed to GeeksforGeeks.org

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