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Area of a square inscribed in a circle which is inscribed in a hexagon
  • Last Updated : 16 Mar, 2021

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

 

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