# Diagonal of a Regular Decagon

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 = 5
Output: 9.51

Input: a = 9
Output: 17.118

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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

Output:

17.118

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