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++ 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 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 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# 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 // 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 ?> |
<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> |
25.3717
Time Complexity: O(1)
Auxiliary Space: O(1)