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Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle

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Given here is an equilateral triangle of side length a, which inscribes a hexagon which in turn inscribes a square. The task is to find the side length of the square.
Examples: 
 

Input:  a = 6
Output: 2.538

Input: a = 8
Output: 3.384


 


 


Approach
We know the, side length of a hexagon inscribed within an equilateral triangle is h = a/3. Please refer Largest hexagon that can be inscribed within an equilateral triangle .
Also, the side length of the square that can be inscribed within a hexagon is x = 1.268h Please refer Largest Square that can be inscribed within a hexagon.
So, side length of the square inscribed within a hexagon which in turn is inscribed within an equilateral triangle, x = 0.423a.
Below is the implementation of the above approach:
 

C++

// C++ program to find the side of the largest square
// that can be inscribed within the hexagon which in return
// is incsribed within an equilateral triangle
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the side
// of the square
float squareSide(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    float x = 0.423 * a;
    return x;
}
 
// Driver code
int main()
{
    float a = 8;
    cout << squareSide(a) << endl;
 
    return 0;
}

                    

Java

// Java program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
class cfg
{
     
// Function to find the side
// of the square
static float squareSide(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    float x = (0.423f * a);
    return x;
}
 
// Driver code
public static void main(String[] args)
{
    float a = 8;
    System.out.println(squareSide(a));
 
}
}
 
// This code is contributed by
// Mukul Singh.

                    

Python3

# Python 3 program to find the side of the
# largest square that can be inscribed
# within the hexagon which in return
# is incsribed within an equilateral triangle
 
# Function to find the side of the square
def squareSide(a):
     
    # Side cannot be negative
    if (a < 0):
        return -1
 
    # side of the square
    x = 0.423 * a
    return x
 
# Driver code
if __name__ == '__main__':
    a = 8
    print(squareSide(a))
 
# This code is contributed by
# Sanjit_Prasad

                    

C#

// C# program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
using System;
 
class GFG
{
     
// Function to find the side
// of the square
static float squareSide(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    float x = (0.423f * a);
    return x;
}
 
// Driver code
public static void Main()
{
    float a = 8;
    Console.WriteLine(squareSide(a));
}
}
 
// This code is contributed by
// shs

                    

PHP

<?php
// PHP program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
 
// Function to find the side of the square
function squareSide($a)
{
 
    // Side cannot be negative
    if ($a < 0)
        return -1;
 
    // side of the square
    $x = 0.423 * $a;
    return $x;
}
 
// Driver code
$a = 8;
echo squareSide($a);
 
// This code is contributed by ajit.
?>

                    

Javascript

<script>
// javascript program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
 
// Function to find the side
// of the square
function squareSide(a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    var x = (0.423 * a);
    return x;
}
 
// Driver code
var a = 8;
document.write(squareSide(a));
 
// This code is contributed by Princi Singh
</script>

                    

Output: 
3.384

 

Time Complexity: O(1) since no loop is used the algorithm takes constant time to finish its execution

Auxiliary Space: O(1) since no extra array is used the space required by the algorithm to complete is constant.



Last Updated : 07 Aug, 2022
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