# Area of hexagon with given diagonal length

You are given the length of the diagonal of a hexagon, d. Your task is to find the area of that hexagon. **Examples:**

Input :5Output :Area of Hexagon: 16.238Input :10Output :Area of Hexagon: 64.9519

**Hexagon**

Hexagon is a regular polygon having six equal sides and all equal angles. The interior angles of Hexagon are of 120 degrees each and the sum of all angles of a Hexagon is 720 degrees.

Let d be the diagonal of Hexagon, then the formula to find the area of Hexagon given by

Area =

**How does above formula work?**

We know that area of hexagon with side length a = (3 âˆš3(a)^{2} ) / 2. Since all sides are of same size and angle is 120 degree, d = 2a or a = d/2. After putting this value, we get area as (3 âˆš3(d)^{2} ) / 8.

Below is the implementation .

## C++

`// C++ program to find the area of Hexagon with given diagonal` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to calculate area` `float` `hexagonArea(` `float` `d)` `{` ` ` `// Formula to find area` ` ` `return` `(3 * ` `sqrt` `(3) * ` `pow` `(d, 2)) / 8;` `}` `// Main` `int` `main()` `{` ` ` `float` `d = 10;` ` ` `cout << ` `"Area of hexagon: "` `<< hexagonArea(d);` ` ` `return` `0;` `}` |

## Java

`// Java program to find the area of ` `// Hexagon with given diagonal ` `import` `java.lang.Math; ` `public` `class` `GfG {` ` ` `// Function to calculate area ` ` ` `public` `static` `float` `hexagonArea(` `float` `d) ` ` ` `{ ` ` ` `// Formula to find area ` ` ` `return` `(` `float` `)((` `3` `* Math.sqrt(` `3` `) * d * d) / ` `8` `); ` ` ` `} ` ` ` `public` `static` `void` `main(String []args) {` ` ` `float` `d = ` `10` `;` ` ` `System.out.println(` `"Area of hexagon: "` `+ hexagonArea(d));` ` ` `}` `}` `// This code is contributed by Rituraj Jain` |

## Python3

`# Python3 program to find the area ` `# of Hexagon with given diagonal ` `from` `math ` `import` `sqrt` `# Function to calculate area ` `def` `hexagonArea(d) :` ` ` `# Formula to find area ` ` ` `return` `(` `3` `*` `sqrt(` `3` `) ` `*` `pow` `(d, ` `2` `)) ` `/` `8` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `d ` `=` `10` ` ` `print` `(` `"Area of hexagon:"` `, ` ` ` `round` `(hexagonArea(d), ` `3` `))` `# This code is contributed by Ryuga` |

## C#

`// C# program to find the area of ` `// Hexagon with given diagonal ` `using` `System;` `public` `class` `GFG{` ` ` ` ` `// Function to calculate area ` ` ` `public` `static` `float` `hexagonArea(` `float` `d) ` ` ` `{ ` ` ` `// Formula to find area ` ` ` `return` `(` `float` `)((3 * Math.Sqrt(3) * d * d) / 8); ` ` ` `} ` `//Code driven` ` ` `static` `public` `void` `Main (){` ` ` `float` `d = 10;` ` ` `Console.WriteLine(` `"Area of hexagon: "` `+ hexagonArea(d));` ` ` `}` `//This code is contributed by Tushil. ` `}` |

## PHP

`<?php` `// PHP program to find the area of` `// Hexagon with given diagonal` `// Function to calculate area` `function` `hexagonArea(` `$d` `)` `{` ` ` `// Formula to find area` ` ` `return` `(3 * sqrt(3) * pow(` `$d` `, 2)) / 8;` `}` `// Driver Code` `$d` `= 10;` `echo` `"Area of hexagon: "` `,` ` ` `hexagonArea(` `$d` `);` `// This code is contributed by ajit.` `?>` |

## Javascript

`<script>` `// JavaScript program to find` `// the area of Hexagon with given diagonal` `// Function to calculate area` `function` `hexagonArea( d)` `{` ` ` `// Formula to find area` ` ` `return` `(3 * Math.sqrt(3) * Math.pow(d, 2)) / 8;` `}` `// Driver Code` ` ` `let d = 10;` ` ` `document.write(` `"Area of hexagon: "` `+ hexagonArea(d).toFixed(3));` ` ` `// This code is contributed by todaysgaurav ` `</script>` |

**Output: **

Area of Hexagon: 64.952

**Time Complexity: **O(1)

**Auxiliary Space: **O(1), since no extra space has been taken.