Given here is an equilateral triangle of side length a, which inscribes a hexagon which in turn inscribes a square. The task is to find the side length of the square.
Examples:
Input: a = 6 Output: 2.538 Input: a = 8 Output: 3.384
Approach:
We know the, side length of a hexagon inscribed within an equilateral triangle is h = a/3. Please refer Largest hexagon that can be inscribed within an equilateral triangle .
Also, the side length of the square that can be inscribed within a hexagon is x = 1.268h Please refer Largest Square that can be inscribed within a hexagon.
So, side length of the square inscribed within a hexagon which in turn is inscribed within an equilateral triangle, x = 0.423a.
Below is the implementation of the above approach:
// C++ program to find the side of the largest square // that can be inscribed within the hexagon which in return // is incsribed within an equilateral triangle #include <bits/stdc++.h> using namespace std;
// Function to find the side // of the square float squareSide( float a)
{ // Side cannot be negative
if (a < 0)
return -1;
// side of the square
float x = 0.423 * a;
return x;
} // Driver code int main()
{ float a = 8;
cout << squareSide(a) << endl;
return 0;
} |
// Java program to find the side of the // largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangle class cfg
{ // Function to find the side // of the square static float squareSide( float a)
{ // Side cannot be negative
if (a < 0 )
return - 1 ;
// side of the square
float x = ( 0 .423f * a);
return x;
} // Driver code public static void main(String[] args)
{ float a = 8 ;
System.out.println(squareSide(a));
} } // This code is contributed by // Mukul Singh. |
# Python 3 program to find the side of the # largest square that can be inscribed # within the hexagon which in return # is incsribed within an equilateral triangle # Function to find the side of the square def squareSide(a):
# Side cannot be negative
if (a < 0 ):
return - 1
# side of the square
x = 0.423 * a
return x
# Driver code if __name__ = = '__main__' :
a = 8
print (squareSide(a))
# This code is contributed by # Sanjit_Prasad |
// C# program to find the side of the // largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangle using System;
class GFG
{ // Function to find the side // of the square static float squareSide( float a)
{ // Side cannot be negative
if (a < 0)
return -1;
// side of the square
float x = (0.423f * a);
return x;
} // Driver code public static void Main()
{ float a = 8;
Console.WriteLine(squareSide(a));
} } // This code is contributed by // shs |
<?php // PHP program to find the side of the // largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangle // Function to find the side of the square function squareSide( $a )
{ // Side cannot be negative
if ( $a < 0)
return -1;
// side of the square
$x = 0.423 * $a ;
return $x ;
} // Driver code $a = 8;
echo squareSide( $a );
// This code is contributed by ajit. ?> |
<script> // javascript program to find the side of the // largest square that can be inscribed // within the hexagon which in return is // incsribed within an equilateral triangle // Function to find the side // of the square function squareSide(a)
{ // Side cannot be negative
if (a < 0)
return -1;
// side of the square
var x = (0.423 * a);
return x;
} // Driver code var a = 8;
document.write(squareSide(a)); // This code is contributed by Princi Singh </script> |
3.384
Time Complexity: O(1) since no loop is used the algorithm takes constant time to finish its execution
Auxiliary Space: O(1) since no extra array is used the space required by the algorithm to complete is constant.