Diagonal de un heptágono regular

Dado un entero a que es el lado de un heptágono regular, la tarea es encontrar e imprimir la longitud de su diagonal. 
 

Ejemplos: 
 

Entrada: a = 6 
Salida: 10.812
Entrada: a = 9 
Salida: 16.218 
 

Enfoque: Sabemos que la suma de los ángulos interiores de un polígono = (n – 2) * 180 donde, n es el no. de lados en el polígono. 
Entonces, la suma de los ángulos interiores del heptágono = 5 * 180 = 900 y cada ángulo interior será 128,58 (aprox.). 
Ahora, tenemos que encontrar BC = 2 * x . Si dibujamos una perpendicular AO en BC , veremos que la perpendicular biseca a BC en BO y OC , ya que los triángulos AOB y AOC son congruentes entre sí. 
Entonces, en el triángulo AOB ,sin(64.29) = x / a ie x = 0.901 * a 
Por lo tanto, la longitud de la diagonal será 2 * x ie 1.802 * a .
A continuación se muestra la implementación del enfoque anterior:
 

// 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 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 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# 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 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

<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>

10.812

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)