Área de un cuadrado inscrito en un círculo que está inscrito en un hexágono

Dado un hexágono regular de lado A , que inscribe una circunferencia de radio r , que a su vez inscribe un cuadrado de lado a . La tarea es encontrar el área de este cuadrado.
Ejemplos : 
 

Input :  A = 5
Output : 37.5

Input : A = 8
Output : 96

Enfoque : 
Sabemos que el radio del círculo inscrito dentro del hexágono es, r=A√3/2 ( Consulte aquí ) 
Además, la longitud del lado del círculo dentro del círculo es, a=√r=√3A/√2 
Entonces, Área del cuadrado, Área=(√3A/√2)^2 
 

// 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 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

# 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# 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 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)
?>

<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>

37.5

Complejidad de tiempo : O(1)

Espacio Auxiliar: O(1)