Given an integer a which is the side of a regular hexagon, the task is to find and print the length of its diagonal.
Examples:
Input: a = 6
Output: 10.38
Input: a = 9
Output: 15.57
Approach: We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the number of sides of the polygon.
So, sum of interior angles of a hexagon = 4 * 180 = 720 and each interior angle will be 120.
Now, we have to find BC = 2 * x. If we draw a perpendicular AO on BC, we will see that the perpendicular bisects BC in BO and OC, as triangles AOB and AOC are congruent to each other.
So, in triangle AOB, sin(60) = x / a i.e. x = 0.866 * a
Therefore, diagonal length will be 2 * x i.e. 1.73 * a.
Below is the implementation of the above approach:
C++
// C++ Program to find the diagonal// of a regular hexagon#include <bits/stdc++.h>using namespace std;// Function to find the diagonal// of a regular hexagonfloat hexDiagonal(float a){ // Side cannot be negative if (a < 0) return -1; // Length of the diagonal float d = 1.73 * a; return d;}// Driver codeint main(){ float a = 9; cout << hexDiagonal(a) << endl; return 0;} |
Java
// Java Program to find the diagonal // of a regular hexagonpublic class GFG{ // Function to find the diagonal // of a regular hexagon static double hexDiagonal(float a) { // Side cannot be negative if (a < 0) return -1; // Length of the diagonal double d = (double)1.73 * a; return d; } // Driver code public static void main(String []args) { float a = 9; System.out.println(hexDiagonal(a)) ; } // This code is contributed by Ryuga} |
Python3
# Python3 Program to find the diagonal# of a regular hexagon# Function to find the diagonal# of a regular hexagondef hexDiagonal(a): # Side cannot be negative if (a < 0): return -1; # Length of the diagonal d = 1.73 * a; return d;# Driver codea = 9;print(hexDiagonal(a));# This code is contributed# by Akanksha Rai |
C#
// C# Program to find the diagonal // of a regular hexagon using System ; public class GFG { // Function to find the diagonal // of a regular hexagon static double hexDiagonal(float a) { // Side cannot be negative if (a < 0) return -1; // Length of the diagonal double d = (double)1.73 * a; return d; } // Driver code public static void Main() { float a = 9; Console.WriteLine(hexDiagonal(a)) ; } // This code is contributed by Subhadeep} |
PHP
<?php// PHP Program to find the diagonal// of a regular hexagon// Function to find the diagonal// of a regular hexagonfunction hexDiagonal($a){ // Side cannot be negative if ($a < 0) return -1; // Length of the diagonal $d = 1.73 * $a; return $d;}// Driver code$a = 9;echo hexDiagonal($a), "\n";// This code is contributed // by akt_mit ?> |
Javascript
<script>// javascript Program to find the diagonal // of a regular hexagon// Function to find the diagonal // of a regular hexagon function hexDiagonal(a) { // Side cannot be negative if (a < 0) return -1; // Length of the diagonal var d = 1.73 * a; return d; } // Driver code var a = 9; document.write(hexDiagonal(a)) ; // This code contributed by Princi Singh </script> |
15.57
Time Complexity: O(1)
Auxiliary Space: O(1)
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