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 

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

Time Complexity: O(1)

Auxiliary Space: O(1)