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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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..

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?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)
?>

chevron_right


Output:

37.5


My Personal Notes arrow_drop_up

Budding Web DeveloperKeen learnerAverage CoderDancer&Social Activist

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.