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: 25.3717Input: 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 <bits/stdc++.h>using namespace std;// Function to find the Area// of the Reuleaux trianglefloat 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 codeint 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 squareimport 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 codepublic 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 squareusing 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
<?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 trianglefunction 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 codevar a= 6;document.write(ReuleauxArea(a) );// This code is contributed by Princi Singh </script> |
Output:
25.3717
Time Complexity: O(1)
Auxiliary Space: O(1)
