Área de un polígono regular de n lados con Radio dado

Dado un polígono regular de N lados con radio (distancia del centro a cualquier vértice) R . La tarea es encontrar el área del polígono.
Ejemplos: 
 

Input : r = 9, N = 6
Output : 210.444

Input : r = 8, N = 7
Output : 232.571

En la figura vemos que el polígono se puede dividir en N triángulos iguales.
Mirando uno de los triángulos, vemos que todo el ángulo en el centro se puede dividir en = 360/N partes.
Entonces, el ángulo t = 180/N .
Mirando dentro de uno de los triángulos, vemos, 
 

h = rcost
a = rsint

Sabemos, 
 

area of the triangle = (base * height)/2 
                     = r2sin(t)cos(t)
                     = r2*sin(2t)/2

Entonces, área del polígono: 
 

A = n * (area of one triangle) 
  = n*r2*sin(2t)/2 
  = n*r2*sin(360/n)/2

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ Program to find the area
// of a regular polygon with given radius
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of a regular polygon
float polyarea(float n, float r)
{
    // Side and radius cannot be negative
    if (r < 0 && n < 0)
        return -1;
 
    // Area
    // degree converted to radians
    float A = ((r * r * n) * sin((360 / n) * 3.14159 / 180)) / 2;
 
    return A;
}
 
// Driver code
int main()
{
    float r = 9, n = 6;
 
    cout << polyarea(n, r) << endl;
 
    return 0;
}

// Java Program to find the area
// of a regular polygon with given radius
 
import java.util.*;
class GFG
{
    // Function to find the area
    // of a regular polygon
    static double polyarea(double n, double r)
    {
        // Side and radius cannot be negative
        if (r < 0 && n < 0)
            return -1;
     
        // Area
        // degree converted to radians
        double A = ((r * r * n) * Math.sin((360 / n) * 3.14159 / 180)) / 2;
     
        return A;
    }
     
    // Driver code
    public static void main(String []args)
    {
        float r = 9, n = 6;
     
        System.out.println(polyarea(n, r));
     
         
    }
}
 
// This code is contributed
// By ihritik (Hritik Raj)

# Python3 Program to find the area
# of a regular polygon with given radius
 
# form math lib import sin function
from math import sin
 
# Function to find the area
# of a regular polygon
def polyarea(n, r) :
     
    # Side and radius cannot be negative
    if (r < 0 and n < 0) :
        return -1
 
    # Area
    # degree converted to radians
    A = (((r * r * n) * sin((360 / n) *
                 3.14159 / 180)) / 2);
 
    return round(A, 3)
 
# Driver code
if __name__ == "__main__" :
 
    r, n = 9, 6
    print(polyarea(n, r))
 
# This code is contributed by Ryuga

// C# Program to find the area
// of a regular polygon with given radius
 
using System;
class GFG
{
    // Function to find the area
    // of a regular polygon
    static double polyarea(double n, double r)
    {
        // Side and radius cannot be negative
        if (r < 0 && n < 0)
            return -1;
     
        // Area
        // degree converted to radians
        double A = ((r * r * n) * Math.Sin((360 / n) * 3.14159 / 180)) / 2;
     
        return A;
    }
     
    // Driver code
    public static void Main()
    {
        float r = 9, n = 6;
     
        Console.WriteLine(polyarea(n, r));
     
         
    }
}
 
// This code is contributed
// By ihritik (Hritik Raj)

<?php
// PHP Program to find the area of a
// regular polygon with given radius
 
// Function to find the area
// of a regular polygon
function polyarea($n, $r)
{
    // Side and radius cannot be negative
    if ($r < 0 && $n < 0)
        return -1;
 
    // Area
    // degree converted to radians
    $A = (($r * $r * $n) * sin((360 / $n) *
                     3.14159 / 180)) / 2;
 
    return $A;
}
 
// Driver code
$r = 9;
$n = 6;
echo polyarea($n, $r)."\n";
 
// This code is contributed by ita_c
?>

<script>
// javascript Program to find the area
// of a regular polygon with given radius
 
// Function to find the area
// of a regular polygon
function polyarea(n , r)
{
    // Side and radius cannot be negative
    if (r < 0 && n < 0)
        return -1;
 
    // Area
    // degree converted to radians
    var A = ((r * r * n) * Math.sin((360 / n) * 3.14159 / 180)) / 2;
 
    return A;
}
 
// Driver code
var r = 9, n = 6;
 
document.write(polyarea(n, r).toFixed(5));
 
 
// This code contributed by Princi Singh
</script>

210.444

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)