Given an integer **a** which is the side of a regular decagon, the task is to find and print the length of its diagonal.

**Examples:**

Input:a = 5Output:9.51Input:a = 9Output:17.118

**Approach:** We know that the sum of interior angles of a polygon = **(n – 2) * 180** where, **n** is the no. of sides in the polygon.

So, sum of interior angles of decagon = **8 * 180 = 1440** and each interior angle will be **144**.

Now, we have to find **BC** = **2 * x**. If we draw a perpendicular **AO** on **BC**, we will see that the perpendicular bisects **BC** in **BO** and **OC**, as triangles **AOB** and **AOC** are congruent to each other.

So, in triangle **AOB**, **sin(72) = x / a** i.e. **x = 0.951 * a**

Therefore, diagonal length will be **2 * x** i.e. **1.902 * a**.

Below is the implementation of the above approach:

## C++

`// C++ program to find the diagonal` `// of a regular decagon` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the diagonal` `// of a regular decagon` `float` `decdiagonal(` `float` `a)` `{` ` ` `// Side cannot be negative` ` ` `if` `(a < 0)` ` ` `return` `-1;` ` ` `// Length of the diagonal` ` ` `float` `d = 1.902 * a;` ` ` `return` `d;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `a = 9;` ` ` `cout << decdiagonal(a) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find the diagonal of a regular decdiagonal` `import` `java.util.*;` `import` `java.lang.*;` `import` `java.io.*;` `public` `class` `GFG {` ` ` `// Function to return the diagonal of a regular decdiagonal` ` ` `static` `double` `decdiagonal(` `double` `a)` ` ` `{` `//side cannot be negative` ` ` `if` `(a<` `0` `)` ` ` `return` `-` `1` `;` ` ` `// length of the diagonal` ` ` `double` `d=` `1.902` `*a;` ` ` ` ` `return` `d;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `a = ` `9` `;` ` ` `System.out.println(decdiagonal(a));` ` ` `}` `}` |

## Python3

`# Python3 program to find the diagonal` `# of a regular decagon` `# Function to return the diagonal` `# of a regular decagon` `def` `decdiagonal(a) :` ` ` `# Side cannot be negative` ` ` `if` `(a < ` `0` `) :` ` ` `return` `-` `1` ` ` `# Length of the diagonal` ` ` `d ` `=` `1.902` `*` `a` ` ` `return` `d` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `a ` `=` `9` ` ` `print` `(decdiagonal(a))` ` ` `# This code is contributed by Ryuga` |

## C#

`// C# program to find the diagonal of a regular decdiagonal` `using` `System;` `public` `class` `GFG {` ` ` `// Function to return the diagonal of a regular decdiagonal` ` ` `static` `double` `decdiagonal(` `double` `a)` ` ` `{` `//side cannot be negative` ` ` `if` `(a<0)` ` ` `return` `-1;` ` ` `// length of the diagonal` ` ` `double` `d=1.902*a;` ` ` ` ` `return` `d;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `a = 9;` ` ` `Console.WriteLine(decdiagonal(a));` ` ` `}` `}` `// This code is contributed by anuj_67..` |

## PHP

`<?php` `// PHP program to find the diagonal` `// of a regular decagon` `// Function to return the diagonal` `// of a regular decagon` `function` `decdiagonal(` `$a` `)` `{` ` ` `// Side cannot be negative` ` ` `if` `(` `$a` `< 0)` ` ` `return` `-1;` ` ` `// Length of the diagonal` ` ` `$d` `= 1.902 * ` `$a` `;` ` ` `return` `$d` `;` `}` `// Driver code` `$a` `= 9;` `echo` `decdiagonal(` `$a` `);` `// This code is contributed by ajit.` `?>` |

## Javascript

`<script>` `// javascript program to find the diagonal of a regular decdiagonal` `// Function to return the diagonal of a regular decdiagonal` `function` `decdiagonal(a)` `{` `// side cannot be negative` `if` `(a < 0)` `return` `-1;` `// length of the diagonal` `var` `d = 1.902*a;` `return` `d;` `}` `// Driver code` `var` `a = 9;` `document.write(decdiagonal(a));` `// This code contributed by Princi Singh` `</script>` |

**Output:**

17.118

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