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 triangle float 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 code int main()
{ float a = 6;
cout << trianglearea(a) << endl;
return 0;
} |
Java
// 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 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 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 hexagon import math
# Function to find the area # of the triangle def 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 code a = 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 hexagon using 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 triangle function 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 triangle function 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)