Area of a square inscribed in a circle which is inscribed in a hexagon

Given a regular hexagon with side A, which inscribes a circle of radius r, which in turn inscribes a square of side a.The task is to find the area of this square.
Examples: 

Input :  A = 5
Output : 37.5

Input : A = 8
Output : 96

Approach: 
We know the radius of the circle inscribed within the hexagon is, r=A?3/2(Please refer here) 
Also, side length of circle within the circle is, a=?r=?3A/?2
So, Area of the Square, Area=(?3A/?2)^2

C++

// C++ Program to find the area of the square
// inscribed within the circle which in turn
// is inscribed in a hexagon
#include <bits/stdc++.h>
using namespace std;

// Function to find the area of the square
float area(float a)
{

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

    // area of the square
    float area = pow((a * sqrt(3)) / (sqrt(2)), 2);
    return area;
}

// Driver code
int main()
{
    float a = 5;
    cout << area(a) << endl;
    return 0;
}

Java

// Java Program to find the area of the square
// inscribed within the circle which in turn
// is inscribed in a hexagon

import java.io.*;

class GFG {

// Function to find the area of the square
static float area(float a)
{

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

    // area of the square
    float area = (float)Math.pow((a * Math.sqrt(3)) / (Math.sqrt(2)), 2);
    return area;
}

// Driver code
    public static void main (String[] args) {
        float a = 5;
    System.out.println( area(a));
    }
}
// This code is contributed by ajit

Python3

# Python 3 Program to find the area
# of the square inscribed within the
# circle which in turn is inscribed
# in a hexagon
from math import pow, sqrt

# Function to find the area
# of the square
def area(a):

    # side of hexagon cannot
    # be negative
    if (a < 0):
        return -1

    # area of the square
    area = pow((a * sqrt(3)) /
                   (sqrt(2)), 2)
    return area

# Driver code
if __name__ == '__main__':
    a = 5
    print("{0:.3}".format(area(a)))

# This code is contributed
# by SURENDRA_GANGWAR

C#

// C# Program to find the area of
// the square inscribed within the
// circle which in turn is inscribed
// in a hexagon
using System;

class GFG
{

// Function to find the area
// of the square
static float area(float a)
{

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

    // area of the square
    float area = (float)Math.Pow((a * Math.Sqrt(3)) /
                                 (Math.Sqrt(2)), 2);
    return area;
}

// Driver code
public static void Main ()
{
    float a = 5;
    Console.WriteLine( area(a));
}
}

// This code is contributed by inder_verma..

PHP

<?php
// PHP Program to find the area
// of the square inscribed within
// the circle which in turn is
// inscribed in a hexagon

// Function to find the area
// of the square
function area($a)
{

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

    // area of the square
    $area = pow(($a * sqrt(3)) /
                (sqrt(2)), 2);
    return $area;
}

// Driver code
$a = 5;
echo area($a) . "\n";

// This code is contributed
// by Akanksha Rai(Abby_akku)
?>

Javascript

<script>

// javascript Program to find the area of the square
// inscribed within the circle which in turn
// is inscribed in a hexagon

// Function to find the area of the square
function area(a)
{

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

    // area of the square
    var area = Math.pow((a * Math.sqrt(3)) / (Math.sqrt(2)), 2);
    return area;
}

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


// This code contributed by shikhasingrajput

</script>

Output:

37.5

Time complexity: O(1)

Auxiliary Space: O(1)