Given side of a square a, the task is to find the side of the largest hexagon that can be inscribed within the given square.
Examples:
Input: a = 6
Output: 3.1056
Input: a = 8
Output: 4.1408
Approach:: Let, the side of the hexagon be x and assume that the side of the square, a gets divided into smaller length b & bigger length c i.e. a = b + c
Now from the figure, we see,
b2 + b2 = x2 which gives b = x / ?2
Now again, d / (2 * x) = cos(30) = ?3 / 2 i.e. d = x?3
And, c2 + c2 = d2 which gives c = d / ?2 = x?3 / ?2
Since, a = b + c. So, a = x / ?2 + x?3 / ?2 = ((1 + ?3) / ?2) * x = 1.932 * x
So, side of the hexagon, x = 0.5176 * a
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest hexagon which// can be inscribed within the given square#include <bits/stdc++.h>using namespace std;// Function to return the side// of the hexagonfloat hexagonside(float a){ // Side cannot be negative if (a < 0) return -1; // Side of the hexagon float x = 0.5176 * a; return x;}// Driver codeint main(){ float a = 6; cout << hexagonside(a) << endl; return 0;} |
Java
// Java Program to find the biggest hexagon which// can be inscribed within the given squareimport java.io.*;class GFG { // Function to return the side// of the hexagonstatic double hexagonside(double a){ // Side cannot be negative if (a < 0) return -1; // Side of the hexagon double x = (0.5176 * a); return x;}// Driver code public static void main (String[] args) { double a = 6; System.out.println (hexagonside(a)); }//This code is contributed by ajit. } |
Python 3
# Python 3 Program to find the biggest # hexagon which can be inscribed within# the given square# Function to return the side# of the hexagondef hexagonside(a): # Side cannot be negative if (a < 0): return -1; # Side of the hexagon x = 0.5176 * a; return x;# Driver codea = 6;print(hexagonside(a));# This code is contributed # by Akanksha Rai |
C#
// C# Program to find the biggest hexagon which // can be inscribed within the given square using System;class GFG{ // Function to return the side // of the hexagon static double hexagonside(double a) { // Side cannot be negative if (a < 0) return -1; // Side of the hexagon double x = (0.5176 * a); return x; } // Driver code public static void Main () { double a = 6; Console.WriteLine(hexagonside(a)); } } // This code is contributed by Ryuga. |
PHP
<?php// PHP Program to find the biggest hexagon which// can be inscribed within the given square// Function to return the side of the hexagonfunction hexagonside($a){ // Side cannot be negative if ($a < 0) return -1; // Side of the hexagon $x = 0.5176 * $a; return $x;}// Driver code$a = 6;echo hexagonside($a);// This code is contributed by akt_mit?> |
Javascript
<script>// Javascript Program to find the biggest hexagon which // can be inscribed within the given square // Function to return the side // of the hexagon function hexagonside(a) { // Side cannot be negative if (a < 0) return -1; // Side of the hexagon let x = 0.5176 * a; return x; } // Driver code let a = 6; document.write(hexagonside(a) + "<br>"); // This code is contributed by Manoj</script> |
Output:
3.1056
Time Complexity: O(1)
Auxiliary Space: O(1)
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