# Area of Reuleaux Triangle

Given an integer **h** which is the side of an equilateral triangle formed by the same vertices as the Reuleaux triangle, the task is to find and print the area of the Reuleaux triangle.

**Examples:**

Input:h = 6Output:25.3717Input:h = 9Output:57.0864

**Approach:** The shape made by the intersection of the three circles **ABC** is the **Reuleaux Triangle** and the triangle formed by the same vertices i.e. **ABC** is an equilateral triangle with side **h**.

Now, Area of sector ACB,

A1 = (Ï€ * h^{2}) / 6

Similarly, Area of sector CBA,A2 = (Ï€ * h^{2}) / 6

And, Area of sector BAC,A3 = (Ï€ * h^{2}) / 6

So,A1 + A2 + A3 = (Ï€ * h^{2}) / 2

Since, the area of the triangle is added thrice in the sum.

So, Area of the Reuleaux Triangle,A = (Ï€ * h^{2}) / 2 – 2 * (Area of equilateral triangle) = (Ï€ – âˆš3) * h^{2}/ 2 = 0.70477 * h^{2}

Below is the implementation of the above approach:

## C++

`// C++ Program to find the area` `// of Reuleaux triangle` `#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 Reuleaux triangle` `public` `class` `GFG` `{` ` ` `// Function to find the Area` ` ` `// of the Reuleaux triangle` ` ` `static` `double` `ReuleauxArea(` `float` `a)` ` ` `{` ` ` ` ` `// Side cannot be negative` ` ` `if` `(a < ` `0` `)` ` ` `return` `-` `1` `;` ` ` ` ` `// Area of the Reuleaux triangle` ` ` `double` `A = (` `double` `)` `0.70477` `* Math.pow(a, ` `2` `);` ` ` `return` `A;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `float` `a = ` `6` `;` ` ` `System.out.println(ReuleauxArea(a)) ;` ` ` `}` ` ` `// This code is contributed by Ryuga` `}` |

## Python3

`# Python3 program to find the area` `# of Reuleaux triangle` `import` `math as mt` `# function to the area of the` `# Reuleaux triangle` `def` `ReuleauxArea(a):` ` ` ` ` `# Side cannot be negative` ` ` `if` `a < ` `0` `:` ` ` `return` `-` `1` ` ` `# Area of the Reauleax triangle` ` ` `return` `0.70477` `*` `pow` `(a, ` `2` `)` `# Driver code` `a ` `=` `6` `print` `(ReuleauxArea(a))` `# This code is contributed` `# by Mohit Kumar ` |

## C#

`// C# Program to find the area ` `// of Reuleaux triangle ` ` ` `using` `System;` `public` `class` `GFG` `{` ` ` `// Function to find the Area ` ` ` `// of the Reuleaux triangle ` ` ` `static` `double` `ReuleauxArea(` `float` `a) ` ` ` `{ ` ` ` ` ` `// Side cannot be negative ` ` ` `if` `(a < 0) ` ` ` `return` `-1; ` ` ` ` ` `// Area of the Reuleaux triangle ` ` ` `double` `A = (` `double` `)0.70477 * Math.Pow(a, 2); ` ` ` `return` `A; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `float` `a = 6; ` ` ` `Console.WriteLine(ReuleauxArea(a)) ; ` ` ` `}` `}` ` ` `// This code is contributed by Subhadeep` |

## PHP

`<?php` `// PHP Program to find the area` `// of Reuleaux triangle` `// 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` `);` `// This code is contributed` `// by Akanksha Rai` |

## Javascript

`<script>` `// javascript Program to find the area` `// of Reuleaux triangle` `// 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

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.