# Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon

Last Updated : 07 Aug, 2022

Given a regular hexagon of side length a which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Examples:

```Input: a = 5
Output: 28.3287

Input: a = 9
Output: 91.7848```

Approach: As the side of the square inscribed within a hexagon is x = 1.268a. Please refer Largest Square that can be inscribed within a hexagon.
Also, in the reuleaux triangle, h = x = 1.268a
So, Area of the reuleaux triangle, A = 0.70477*h^2 = 0.70477*(1.268a)^2.
Below is the implementation of the above approach:

## C++

 `// C++ Program to find the biggest Reuleaux triangle` `// inscribed within in a square which in turn` `// is inscribed within a hexagon` `#include ` `using` `namespace` `std;`   `// Function to find the biggest reuleaux triangle` `float` `Area(``float` `a)` `{`   `    ``// side cannot be negative` `    ``if` `(a < 0)` `        ``return` `-1;`   `    ``// height of the reuleaux triangle` `    ``float` `h = 1.268 * a;`   `    ``// area of the reuleaux triangle` `    ``float` `A = 0.70477 * ``pow``(h, 2);`   `    ``return` `A;` `}`   `// Driver code` `int` `main()` `{` `    ``float` `a = 5;` `    ``cout << Area(a) << endl;`   `    ``return` `0;` `}`

## Java

 `// Java Program to find the biggest Reuleaux triangle` `// inscribed within in a square which in turn` `// is inscribed within a hexagon`   `import` `java.io.*;`   `class` `GFG ` `{`   `// Function to find the biggest reuleaux triangle` `static` `float` `Area(``float` `a)` `{`   `    ``// side cannot be negative` `    ``if` `(a < ``0``)` `        ``return` `-``1``;`   `    ``// height of the reuleaux triangle` `    ``float` `h =(``float``) ``1.268` `* a;`   `    ``// area of the reuleaux triangle` `    ``float` `A = (``float``)(``0.70477` `* Math.pow(h, ``2``));`   `    ``return` `A;` `}`   `    ``// Driver code` `    ``public` `static` `void` `main (String[] args) ` `    ``{` `        ``float` `a = ``5``;` `    ``System.out.println( Area(a));` `    ``}` `}`   `// This code is contributed by anuj_67`

## Python3

 `# Python3 Program to find the biggest ` `# Reuleaux triangle inscribed within` `# in a square which in turn is` `# inscribed within a hexagon` `import` `math`   `# Function to find the biggest ` `# reuleaux triangle` `def` `Area(a):`   `    ``# side cannot be negative` `    ``if` `(a < ``0``):` `        ``return` `-``1`   `    ``# height of the reuleaux triangle` `    ``h ``=` `1.268` `*` `a`   `    ``# area of the reuleaux triangle` `    ``A ``=` `0.70477` `*` `math.``pow``(h, ``2``)`   `    ``return` `A`   `# Driver code` `a ``=` `5` `print``(Area(a),end ``=` `"\n"``)`   `# This code is contributed ` `# by Akanksha Rai`

## C#

 `// C# Program to find the biggest Reuleaux` `// triangle inscribed within in a square ` `// which in turn is inscribed within a hexagon` `using` `System;`   `class` `GFG ` `{`   `// Function to find the biggest reuleaux triangle` `static` `float` `Area(``float` `a)` `{`   `    ``// side cannot be negative` `    ``if` `(a < 0)` `        ``return` `-1;`   `    ``// height of the reuleaux triangle` `    ``float` `h =(``float``) 1.268 * a;`   `    ``// area of the reuleaux triangle` `    ``float` `A = (``float``)(0.70477 * Math.Pow(h, 2));`   `    ``return` `A;` `}`   `// Driver code` `public` `static` `void` `Main () ` `{` `    ``float` `a = 5;` `    ``Console.WriteLine(Area(a));` `}` `}`   `// This code is contributed ` `// by Akanksha Rai`

## PHP

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## Javascript

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Output:

`28.3287`

Time complexity: O(1)

Auxiliary Space: O(1)

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