Diagonal of a Regular Heptagon

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

Examples:

Input: a = 6 
Output: 10.812
Input: a = 9 
Output: 16.218 

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 heptagon = 5 * 180 = 900 and each interior angle will be 128.58(Approx). 
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(64.29) = x / a i.e. x = 0.901 * a
Therefore, diagonal length will be 2 * x i.e. 1.802 * a.
Below is the implementation of the above approach:

C++

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

// Function to return the diagonal
// of a regular heptagon
float heptdiagonal(float a)
{

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

    // Length of the diagonal
    float d = 1.802 * a;
    return d;
}

// Driver code
int main()
{
    float a = 6;
    cout << heptdiagonal(a) << endl;
    return 0;
}

Java

// Java program to find the diagonal of a regular heptagon
import java.util.*;
import java.lang.*;
import java.io.*;

public class GFG {

    // Function to return the diagonal of a regular heptagon
    static double heptdiagonal(double a)
    {

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

        // length of the diagonal
        double d=1.802*a;

        return d;
    }

    // Driver code
    public static void main(String[] args)
    {
        int a = 6;
        System.out.println(heptdiagonal(a));
    }
}

Python3

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

# Function to return the diagonal
# of a regular heptagon
def heptdiagonal(a) :

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

    # Length of the diagonal
    d = 1.802 * a

    return round(d, 3)

# Driver code
if __name__ == "__main__" :

    a = 6
    print(heptdiagonal(a))

# This code is contributed by Ryuga

C#

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

    // Function to return the diagonal of a regular heptagon
    static double heptdiagonal(double a)
    {

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

        // length of the diagonal
        double d=1.802*a;

        return d;
    }

    // Driver code
    public static void Main()
    {
        int a = 6;
        Console.WriteLine(heptdiagonal(a));
    }
} // This code is contributed by Mukul singh

PHP

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

// Function to return the diagonal
// of a regular heptagon
function heptdiagonal($a)
{

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

    // Length of the diagonal
    $d = 1.802 * $a;
    return $d;
}

// Driver code
$a = 6;
echo heptdiagonal($a);

// This code is contributed
// by Akanksha Rai

Javascript

<script>
// javascript program to find the diagonal of a regular heptagon

    // Function to return the diagonal of a regular heptagon
    function heptdiagonal(a)
    {

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

        // length of the diagonal
        var d = 1.802*a;

        return d;
    }

// Driver code
var a = 6;
document.write(heptdiagonal(a).toFixed(5));

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

Output:

10.812

Time Complexity: O(1)

Auxiliary Space: O(1)