# 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.

**Examples:**

Input:a = 6

Output:25.3717

Input:a = 8

Output:45.1053

**Approach**: We know that the Area of Reuleaux Traingle 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; ` `} ` |

*chevron_right*

*filter_none*

## 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. ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` |

*chevron_right*

*filter_none*

## 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 ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

25.3717

## Recommended Posts:

- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Biggest Reuleaux Triangle within a Square which is inscribed within a Circle
- Biggest Reuleaux Triangle inscirbed within a square inscribed in a semicircle
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Biggest Square that can be inscribed within an Equilateral triangle
- Area of Reuleaux Triangle
- Area of a largest square fit in a right angle triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Check if a number is perfect square without finding square root
- The biggest possible circle that can be inscribed in a rectangle
- Count square and non-square numbers before n
- Biggest integer which has maximum digit sum in range from 1 to n

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.