Open In App

# 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 Triangle is 0.70477 * b2 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 * a2

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 ``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 reuleaux 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

 ``

## Javascript

 ``

Output:

`25.3717`

Time Complexity: O(1)

Auxiliary Space: O(1)