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

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 = 6Output:2.538Input:a = 8Output: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; ` `} ` |

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## 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. ` |

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## 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 ` |

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## 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
[tabby title="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. ` `?> ` |

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**Output:**

3.384

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