# 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 √3(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 √3(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; ` `} ` |

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## 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 ` |

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## 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 ode ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `d ` `=` `10` ` ` `print` `(` `"Area of hexagon:"` `, ` ` ` `round` `(hexagonArea(d), ` `3` `)) ` ` ` `# This code is contributed by Ryuga ` |

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## 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. ` `} ` |

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## 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. ` `?> ` |

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**Output:**

Area of Hexagon: 64.952

**Time Complexity: **O(1)

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