Area of a n-sided regular polygon with given side length

Given a regular polygon of N sides with side length a. The task is to find the area of the polygon. 
Examples:

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

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

Approach: In the figure above, we see the polygon can be divided into N equal triangles. Looking into one of the triangles, we see that the whole angle at the center can be divided into = 360/N
So, angle t = 180/n
Now, tan(t) = a/2*h
So, h = a/(2*tan(t))
Area of each triangle = (base * height)/2 = a * a/(4*tan(t))
So, area of the polygon, 

A = n * (area of one triangle) = a2 * n/(4tan t)

Below is the implementation of the above approach: 

C++

// C++ Program to find the area of a regular
// polygon with given side length

#include <bits/stdc++.h>
using namespace std;

// Function to find the area
// of a regular polygon
float polyarea(float n, float a)
{
    // Side and side length cannot be negative
    if (a < 0 && n < 0)
        return -1;

    // Area
    // degree converted to radians
    float A = (a * a * n) / (4 * tan((180 / n) * 3.14159 / 180));

    return A;
}

// Driver code
int main()
{
    float a = 9, n = 6;

    cout << polyarea(n, a) << endl;

    return 0;
}

Java

// Java  Program to find the area of a regular
// polygon with given side length

import java.io.*;

class GFG {


// Function to find the area
// of a regular polygon
static float polyarea(float n, float a)
{
    // Side and side length cannot be negative
    if (a < 0 && n < 0)
        return -1;

    // Area
    // degree converted to radians
    float A = (a * a * n) /(float) (4 * Math.tan((180 / n) * 3.14159 / 180));

    return A;
}

// Driver code

    public static void main (String[] args) {
    float a = 9, n = 6;

    System.out.println( polyarea(n, a));
    }
}
// This code is contributed by inder_verma..

Python3

# Python 3 Program to find the area
# of a regular polygon with given
# side length
from math import tan

# Function to find the area of a
# regular polygon
def polyarea(n, a):

    # Side and side length cannot
    # be negative
    if (a < 0 and n < 0):
        return -1

    # Area degree converted to radians
    A = (a * a * n) / (4 * tan((180 / n) *
                      3.14159 / 180))

    return A

# Driver code
if __name__ == '__main__':
    a = 9
    n = 6

    print('{0:.6}'.format(polyarea(n, a)))

# This code is contributed by
# Shashank_sharma

C#

// C# Program to find the area of a regular
// polygon with given side length
using System;

class GFG
{

// Function to find the area
// of a regular polygon
static float polyarea(float n, float a)
{
    // Side and side length cannot be negative
    if (a < 0 && n < 0)
        return -1;

    // Area
    // degree converted to radians
    float A = (a * a * n) / (float)(4 * Math.Tan((180 / n) *
                                           3.14159 / 180));

    return A;
}

// Driver code
public static void Main ()
{
    float a = 9, n = 6;

    Console.WriteLine(polyarea(n, a));
}
}

// This code is contributed
// by Akanksha Rai

PHP

<?php
// PHP Program to find the area of a regular
// polygon with given side length

// Function to find the area
// of a regular polygon
function polyarea($n, $a)
{
    // Side and side length cannot
    // be negative
    if ($a < 0 && $n < 0)
        return -1;

    // Area
    // degree converted to radians
    $A = ($a * $a * $n) / (4 * tan((180 / $n) *
                              3.14159 / 180));

    return $A;
}

// Driver code
$a = 9 ;
$n = 6 ;

echo round(polyarea($n, $a), 3);

// This code is contributed by Ryuga
?>

Javascript

<script>
// javascript  Program to find the area of a regular
// polygon with given side length

// Function to find the area
// of a regular polygon
function polyarea(n , a)
{

    // Side and side length cannot be negative
    if (a < 0 && n < 0)
        return -1;

    // Area
    // degree converted to radians
    var A = (a * a * n) / (4 * Math.tan((180 / n) * 3.14159 / 180));

    return A;
}

// Driver code
var a = 9, n = 6;
document.write( polyarea(n, a).toFixed(5));

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

Output:

210.444

Time Complexity: O(1)

Auxiliary Space: O(1)