Given an ellipse with major axis length and minor axis **2a** & **2b** respectively 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, b = 4Output:0.0722389Input:a = 7, b = 11Output:0.0202076

**Approach**: As, the side of the square inscribed within an ellipse is, **x = √(a^2 + b^2)/ab.** Please refer Area of the Largest square that can be inscribed in an ellipse.

Also, in the reuleaux triangle, **h = x = √(a^2 + b^2)/ab**.

So, Area of the reuleaux triangle, **A = 0.70477*h^2 = 0.70477*((a^2 + b^2)/a^2b^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 an ellipse ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the biggest reuleaux triangle ` `float` `Area(` `float` `a, ` `float` `b) ` `{ ` ` ` ` ` `// length of the axes cannot be negative ` ` ` `if` `(a < 0 && b < 0) ` ` ` `return` `-1; ` ` ` ` ` `// height of the reuleaux triangle ` ` ` `float` `h = ` `sqrt` `(((` `pow` `(a, 2) + ` `pow` `(b, 2)) ` ` ` `/ (` `pow` `(a, 2) * ` `pow` `(b, 2)))); ` ` ` ` ` `// area of the reuleaux triangle ` ` ` `float` `A = 0.70477 * ` `pow` `(h, 2); ` ` ` ` ` `return` `A; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `a = 5, b = 4; ` ` ` `cout << Area(a, b) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find the biggest Reuleaux triangle ` `// inscribed within in a square which in turn ` `// is inscribed within an ellipse ` `import` `java.io.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the biggest reuleaux triangle ` `static` `float` `Area(` `float` `a, ` `float` `b) ` `{ ` ` ` ` ` `// length of the axes cannot be negative ` ` ` `if` `(a < ` `0` `&& b < ` `0` `) ` ` ` `return` `-` `1` `; ` ` ` ` ` `// height of the reuleaux triangle ` ` ` `float` `h = (` `float` `)Math.sqrt(((Math.pow(a, ` `2` `) + Math.pow(b, ` `2` `)) ` ` ` `/ (Math.pow(a, ` `2` `) * Math.pow(b, ` `2` `)))); ` ` ` ` ` `// 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` `, b = ` `4` `; ` ` ` `System.out.println(Area(a, b)); ` `} ` `} ` ` ` `// This code is contributed by anuj_67.. ` |

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## Python3

`# Python3 Program to find the biggest Reuleaux ` `# triangle inscribed within in a square ` `# which in turn is inscribed within an ellipse ` `import` `math; ` ` ` `# Function to find the biggest ` `# reuleaux triangle ` `def` `Area(a, b): ` ` ` ` ` `# length of the axes cannot ` ` ` `# be negative ` ` ` `if` `(a < ` `0` `and` `b < ` `0` `): ` ` ` `return` `-` `1` `; ` ` ` ` ` `# height of the reuleaux triangle ` ` ` `h ` `=` `math.sqrt(((` `pow` `(a, ` `2` `) ` `+` `pow` `(b, ` `2` `)) ` `/` ` ` `(` `pow` `(a, ` `2` `) ` `*` `pow` `(b, ` `2` `)))); ` ` ` ` ` `# area of the reuleaux triangle ` ` ` `A ` `=` `0.70477` `*` `pow` `(h, ` `2` `); ` ` ` ` ` `return` `A; ` ` ` `# Driver code ` `a ` `=` `5` `; ` `b ` `=` `4` `; ` `print` `(` `round` `(Area(a, b), ` `7` `)); ` ` ` `# This code is contributed by chandan_jnu ` |

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## C#

`// C# Program to find the biggest Reuleaux triangle ` `// inscribed within in a square which in turn ` `// is inscribed within an ellipse ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the biggest reuleaux triangle ` `static` `double` `Area(` `double` `a, ` `double` `b) ` `{ ` ` ` ` ` `// length of the axes cannot be negative ` ` ` `if` `(a < 0 && b < 0) ` ` ` `return` `-1; ` ` ` ` ` `// height of the reuleaux triangle ` ` ` `double` `h = (` `double` `)Math.Sqrt(((Math.Pow(a, 2) + ` ` ` `Math.Pow(b, 2)) / ` ` ` `(Math.Pow(a, 2) * ` ` ` `Math.Pow(b, 2)))); ` ` ` ` ` `// area of the reuleaux triangle ` ` ` `double` `A = (` `double` `)(0.70477 * Math.Pow(h, 2)); ` ` ` ` ` `return` `A; ` `} ` ` ` `// Driver code ` `static` `void` `Main() ` `{ ` ` ` `double` `a = 5, b = 4; ` ` ` `Console.WriteLine(Math.Round(Area(a, b),7)); ` `} ` `} ` ` ` `// This code is contributed by chandan_jnu ` |

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## PHP

`<?php ` `// PHP Program to find the biggest Reuleaux ` `// triangle inscribed within in a square ` `// which in turn is inscribed within an ellipse ` ` ` `// Function to find the biggest ` `// reuleaux triangle ` `function` `Area(` `$a` `, ` `$b` `) ` `{ ` ` ` ` ` `// length of the axes cannot ` ` ` `// be negative ` ` ` `if` `(` `$a` `< 0 && ` `$b` `< 0) ` ` ` `return` `-1; ` ` ` ` ` `// height of the reuleaux triangle ` ` ` `$h` `= sqrt(((pow(` `$a` `, 2) + pow(` `$b` `, 2)) / ` ` ` `(pow(` `$a` `, 2) * pow(` `$b` `, 2)))); ` ` ` ` ` `// area of the reuleaux triangle ` ` ` `$A` `= 0.70477 * pow(` `$h` `, 2); ` ` ` ` ` `return` `$A` `; ` `} ` ` ` `// Driver code ` `$a` `= 5; ` `$b` `= 4; ` `echo` `round` `(Area(` `$a` `, ` `$b` `), 7); ` ` ` `// This code is contributed by Ryuga ` `?> ` |

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**Output:**

0.0722389

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