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 = 6
Output: 25.3717
Input: h = 9
Output: 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 = (? * h2) / 6
Similarly, Area of sector CBA, A2 = (? * h2) / 6
And, Area of sector BAC, A3 = (? * h2) / 6
So, A1 + A2 + A3 = (? * h2) / 2
Since, the area of the triangle is added thrice in the sum.
So, Area of the Reuleaux Triangle, A = (? * h2) / 2 – 2 * (Area of equilateral triangle) = (? – ?3) * h2 / 2 = 0.70477 * h2
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 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 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 triangleimport math as mt# function to the area of the # Reuleaux triangledef ReuleauxArea(a): # Side cannot be negative if a < 0: return -1 # Area of the Reauleax triangle return 0.70477 * pow(a, 2)# Driver codea = 6print(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 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);// 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> |
25.3717
Time Complexity: O(1)
Auxiliary Space: O(1)
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