# Biggest Reuleaux Triangle within A Square

Given an integer **a** which is the side of a square, the task is to find the biggest Reuleaux Triangle that can be inscribed within it.

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**Examples:**

Input:a = 6Output:25.3717

Input:a = 8Output:45.1053

**Approach**: We know that the Area of Reuleaux Triangle is **0.70477 * b ^{2}** where

**b**is the distance between the parallel lines supporting the Reuleaux Triangle.

From the figure, it is clear that distance between parallel lines supporting the Reuleaux Triangle = Side of the square i.e.

**a**

So, Area of the Reuleaux Triangle,

**A = 0.70477 * a**

^{2}Below is the implementation of the above approach:

## C++

`// C++ Program to find the area` `// of the biggest Reuleaux triangle` `// that can be inscribed within a square` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the Area` `// of the Reuleaux triangle` `float` `ReuleauxArea(` `float` `a)` `{` ` ` `// Side cannot be negative` ` ` `if` `(a < 0)` ` ` `return` `-1;` ` ` `// Area of the Reuleaux triangle` ` ` `float` `A = 0.70477 * ` `pow` `(a, 2);` ` ` `return` `A;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `a = 6;` ` ` `cout << ReuleauxArea(a) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java Program to find the area` `// of the biggest Reuleaux triangle` `// that can be inscribed within a square` `import` `java.lang.Math;` `class` `cfg` `{` `// Function to find the Area` `// of the Reuleaux triangle` ` ` `static` `double` `ReuleauxArea(` `double` `a)` `{` ` ` `// Side cannot be negative` ` ` `if` `(a < ` `0` `)` ` ` `return` `-` `1` `;` ` ` `// Area of the Reuleaux triangle` ` ` `double` `A = ` `0.70477` `* Math.pow(a, ` `2` `);` ` ` `return` `A;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `double` `a= ` `6` `;` ` ` `System.out.println(ReuleauxArea(a) );` ` ` `}` `}` `//This code is contributed by Mukul Singh.` |

## Python3

`# Python3 Program to find the area` `# of the biggest Reuleaux triangle` `# that can be inscribed within a square` `# Function to find the Area` `# of the Reuleaux triangle` `def` `ReuleauxArea(a) :` ` ` `# Side cannot be negative` ` ` `if` `(a < ` `0` `) :` ` ` `return` `-` `1` ` ` `# Area of the Reuleaux triangle` ` ` `A ` `=` `0.70477` `*` `pow` `(a, ` `2` `);` ` ` `return` `A` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `a ` `=` `6` ` ` `print` `(ReuleauxArea(a))` `# This code is contributed by Ryuga` |

## C#

`// C# program to find area of the` `//biggest Reuleaux triangle that can be inscribed` `//within a square` `using` `System;` ` ` `class` `GFG {` ` ` ` ` `// Function to find the area` ` ` `// of the reuleaux triangle` ` ` `static` `double` `reuleauxArea(` `double` `a)` ` ` `{` ` ` ` ` `//Side cannot be negative` ` ` `if` `(a<0)` ` ` `return` `-1;` ` ` ` ` `// Area of the reauleaux triangle` ` ` `double` `A=0.70477*Math.Pow(a,2);` ` ` `return` `A;` ` ` `}` ` ` ` ` `// Driver code` ` ` `static` `public` `void` `Main()` ` ` `{` ` ` `double` `a= 6;` ` ` `Console.WriteLine(reuleauxArea( a));` ` ` `}` `}` `//This code is contributed by Mohit kumar 29` |

## PHP

`<?php` `// PHP Program to find the area of the` `// biggest Reuleaux triangle that can` `// be inscribed within a square` `// Function to find the Area` `// of the Reuleaux triangle` `function` `ReuleauxArea(` `$a` `)` `{` ` ` `// Side cannot be negative` ` ` `if` `(` `$a` `< 0)` ` ` `return` `-1;` ` ` `// Area of the Reuleaux triangle` ` ` `$A` `= 0.70477 * pow(` `$a` `, 2);` ` ` `return` `$A` `;` `}` `// Driver code` `$a` `= 6;` `echo` `ReuleauxArea(` `$a` `) . ` `"\n"` `;` `// This code is contributed by ita_c` `?>` |

## Javascript

`<script>` `// javascript Program to find the area` `// of the biggest Reuleaux triangle` `// that can be inscribed within a square` `// Function to find the Area` `// of the Reuleaux triangle` ` ` `function` `ReuleauxArea(a)` `{` ` ` `// Side cannot be negative` ` ` `if` `(a < 0)` ` ` `return` `-1;` ` ` `// Area of the Reuleaux triangle` ` ` `var` `A = 0.70477 * Math.pow(a, 2);` ` ` `return` `A;` `}` `// Driver code` `var` `a= 6;` `document.write(ReuleauxArea(a) );` `// This code is contributed by Princi Singh` `</script>` |

**Output:**

25.3717