# Largest hexagon that can be inscribed within an equilateral triangle

• Last Updated : 25 Jun, 2022

Given an equilateral triangle of side length a, the task is to find the largest hexagon that can be inscribed within it.
Examples:

Input: a = 6
Output: 2
Input: a = 9
Output: Approach: From the figure, it is clear that the three small triangles are also equilateral. So they will have side length b = a / 3 where b is also the length of the hexagon and a is the length of the given equilateral triangle.
Below is the implementation of the above approach:

## C++

 `// C++ program to find the side of the``// largest hexagon which can be inscribed``// within an equilateral triangle``#include ``using` `namespace` `std;` `// Function to find the side``// of the hexagon``float` `hexagonside(``float` `a)``{` `    ``// Side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;` `    ``// Side of the hexagon``    ``float` `x = a / 3;``    ``return` `x;``}` `// Driver code``int` `main()``{``    ``float` `a = 6;``    ``cout << hexagonside(a) << endl;``    ``return` `0;``}`

## Java

 `// Java program to find the side of the``// largest hexagon which can be inscribed``// within an equilateral triangle``class` `CLG``{``// Function to find the side``// of the hexagon`` ``static` `float` `hexagonside(``float` `a)``{` `    ``// Side cannot be negative``    ``if` `(a < ``0``)``        ``return` `-``1``;` `    ``// Side of the hexagon``    ``float` `x = a / ``3``;``    ``return` `x;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``float` `a = ``6``;``    ``System.out.println(hexagonside(a));``    ` `}``}`

## Python3

 `# Python3 program to find the side of the``# largest hexagon which can be inscribed``# within an eqilateral triangle` `# function to find the side of the hexagon``def` `hexagonside(a):``    ` `    ``# Side cannot be negative``    ``if` `a < ``0``:``        ``return` `-``1``        ` `    ``# Side of the hexagon``    ``x ``=` `a ``/``/` `3``    ``return` `x` `# Driver code``a ``=` `6``print``(hexagonside(a))` `# This code is contributed``# by Mohit kumar 29`

## C#

 `using` `System;``// C# program to find the side of the``// largest hexagon which can be inscribed``// within an equilateral triangle``class` `CLG``{``// Function to find the side``// of the hexagon`` ``static` `float` `hexagonside(``float` `a)``{`` ` `    ``// Side cannot be negative``    ``if` `(a < 0)``        ``return` `-1;`` ` `    ``// Side of the hexagon``    ``float` `x = a / 3;``    ``return` `x;``}`` ` `// Driver code``public` `static` `void` `Main()``{``    ``float` `a = 6;``    ``Console.Write(hexagonside(a));``     ` `}``}`

## PHP

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## Javascript

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Output:

`2`

Time Complexity: O(1)

Auxiliary Space: O(1)

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