Given here is a regular hexagon, of side length a, the task is to find the area of the biggest triangle that can be inscribed within it.
Examples:
Input: a = 6 Output: area = 46.7654 Input: a = 8 Output: area = 83.1384
Approach:
It is very clear that the biggest triangle that can be inscribed within the hexagon is an equilateral triangle.
In triangle ACD,
following Pythagoras theorem,
(a/2)^2 + (b/2)^2 = a^2
b^2/4 = 3a^2/4
So, b = a?3
Therefore, area of the triangle, A = ?3(a?3)^2/4= 3?3a^2/4
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest triangle// which can be inscribed within the hexagon#include <bits/stdc++.h>using namespace std;// Function to find the area// of the trianglefloat trianglearea(float a){ // side cannot be negative if (a < 0) return -1; // area of the triangle float area = (3 * sqrt(3) * pow(a, 2)) / 4; return area;}// Driver codeint main(){ float a = 6; cout << trianglearea(a) << endl; return 0;} |
Java
// Java Program to find the biggest triangle// which can be inscribed within the hexagonimport java.io.*;class GFG { // Function to find the area// of the trianglestatic double trianglearea(double a){ // side cannot be negative if (a < 0) return -1; // area of the triangle double area = (3 * Math.sqrt(3) * Math.pow(a, 2)) / 4; return area;} public static void main (String[] args) { double a = 6; System.out.println (trianglearea(a)); }//This Code is contributed by Sachin.. } |
Python3
# Python3 Program to find the biggest triangle# which can be inscribed within the hexagonimport math# Function to find the area# of the triangledef trianglearea(a): # side cannot be negative if (a < 0): return -1; # area of the triangle area = (3 * math.sqrt(3) * math.pow(a, 2)) / 4; return area;# Driver codea = 6;print(trianglearea(a))# This code is contributed # by Akanksha Rai |
C#
// C# Program to find the biggest triangle // which can be inscribed within the hexagonusing System;class GFG { // Function to find the area // of the triangle static double trianglearea(double a) { // side cannot be negative if (a < 0) return -1; // area of the triangle double area = (3 * Math.Sqrt(3) * Math.Pow(a, 2)) / 4; return Math.Round(area,4); } public static void Main () { double a = 6; Console.WriteLine(trianglearea(a)); } // This code is contributed by Ryuga} |
PHP
<?php// PHP Program to find the biggest triangle// which can be inscribed within the hexagon// Function to find the area// of the trianglefunction trianglearea($a){ // side cannot be negative if ($a < 0) return -1; // area of the triangle $area = (3 * sqrt(3) * pow($a, 2)) / 4; return $area;}// Driver code$a = 6;echo trianglearea($a);// This code is contributed // by inder_verma?> |
Javascript
<script>// javascript Program to find the biggest triangle// which can be inscribed within the hexagon // Function to find the area// of the trianglefunction trianglearea(a){ // side cannot be negative if (a < 0) return -1; // area of the triangle var area = (3 * Math.sqrt(3) * Math.pow(a, 2)) / 4; return area.toFixed(4);}var a = 6;document.write(trianglearea(a));// This code contributed by Princi Singh </script> |
Output:
46.7654
Time complexity: O(1)
Auxiliary Space: O(1)
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