Diagonal of a Regular Hexagon

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

Input: a = 6 
Output: 10.38
Input: a = 9 
Output: 15.57 

Approach: We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the number of sides of the polygon. 
So, sum of interior angles of a hexagon = 4 * 180 = 720 and each interior angle will be 120. 
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(60) = x / a i.e. x = 0.866 * a
Therefore, diagonal length will be 2 * x i.e. 1.73 * a.
Below is the implementation of the above approach: 

C++

// C++ Program to find the diagonal
// of a regular hexagon
#include <bits/stdc++.h>
using namespace std;

// Function to find the diagonal
// of a regular hexagon
float hexDiagonal(float a)
{

    // Side cannot be negative
    if (a < 0)
        return -1;

    // Length of the diagonal
    float d = 1.73 * a;
    return d;
}

// Driver code
int main()
{
    float a = 9;
    cout << hexDiagonal(a) << endl;
    return 0;
}

Java

// Java Program to find the diagonal
// of a regular hexagon

public class GFG
{

    // Function to find the diagonal
    // of a regular hexagon
    static double hexDiagonal(float a)
    {

        // Side cannot be negative
        if (a < 0)
            return -1;

        // Length of the diagonal
        double d = (double)1.73 * a;
        return d;
    }

    // Driver code
    public static void main(String []args)
    {
        float a = 9;
        System.out.println(hexDiagonal(a)) ;
    }
    // This code is contributed by Ryuga
}

Python3

# Python3 Program to find the diagonal
# of a regular hexagon

# Function to find the diagonal
# of a regular hexagon
def hexDiagonal(a):

    # Side cannot be negative
    if (a < 0):
        return -1;

    # Length of the diagonal
    d = 1.73 * a;
    return d;


# Driver code
a = 9;
print(hexDiagonal(a));

# This code is contributed
# by Akanksha Rai

C#

// C# Program to find the diagonal
// of a regular hexagon
using System ;
public class GFG
{

    // Function to find the diagonal
    // of a regular hexagon
    static double hexDiagonal(float a)
    {

        // Side cannot be negative
        if (a < 0)
            return -1;

        // Length of the diagonal
        double d = (double)1.73 * a;
        return d;
    }

    // Driver code
    public static void Main()
    {
        float a = 9;
        Console.WriteLine(hexDiagonal(a)) ;
    }
    // This code is contributed by Subhadeep
}

PHP

<?php
// PHP Program to find the diagonal
// of a regular hexagon

// Function to find the diagonal
// of a regular hexagon
function hexDiagonal($a)
{

    // Side cannot be negative
    if ($a < 0)
        return -1;

    // Length of the diagonal
    $d = 1.73 * $a;
    return $d;
}

// Driver code
$a = 9;
echo hexDiagonal($a), "\n";

// This code is contributed
// by akt_mit
?>

Javascript

<script>
// javascript Program to find the diagonal
// of a regular hexagon

// Function to find the diagonal
// of a regular hexagon
function hexDiagonal(a)
{

    // Side cannot be negative
    if (a < 0)
        return -1;

    // Length of the diagonal
    var d = 1.73 * a;
    return d;
}

    // Driver code
var a = 9;
document.write(hexDiagonal(a)) ;

// This code contributed by Princi Singh
</script>

Output:

15.57

Time Complexity: O(1)

Auxiliary Space: O(1)