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Biggest Reuleaux Triangle within A Square

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  • Last Updated : 25 Jun, 2022
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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 <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 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 reauleaux 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 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) . "\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 code
var 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)


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