Area of the Largest Triangle inscribed in a Hexagon - GeeksforGeeks

11 Nov, 2021
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++
Java
Python3
C#
PHP
Javascript
// 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 Program to find the biggest triangle// which can be inscribed within the hexagon import 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 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# Program to find the biggest triangle// which can be inscribed within the hexagon using System; 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 Math.Round(area,4);}     public static void Main () {        double a = 6;        Console.WriteLine(trianglearea(a));     }        // This code is contributed by Ryuga }
<?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?>
<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>
46.7654
 
Sach_Code
ankthon
inderDuMCA
Akanksha_Rai
princi singh
clintra
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Mathematical
Mathematical
Geometric
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