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Largest hexagon that can be inscribed within an equilateral triangle

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  • Last Updated : 25 Jun, 2022
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Given an equilateral triangle of side length a, the task is to find the largest hexagon that can be inscribed within it.
Examples: 
 

Input: a = 6 
Output: 2
Input: a = 9 
Output:
 

 

 

Approach: From the figure, it is clear that the three small triangles are also equilateral. So they will have side length b = a / 3 where b is also the length of the hexagon and a is the length of the given equilateral triangle.
Below is the implementation of the above approach: 
 

C++




// C++ program to find the side of the
// largest hexagon which can be inscribed
// within an equilateral triangle
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the side
// of the hexagon
float hexagonside(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    float x = a / 3;
    return x;
}
 
// Driver code
int main()
{
    float a = 6;
    cout << hexagonside(a) << endl;
    return 0;
}

Java




// Java program to find the side of the
// largest hexagon which can be inscribed
// within an equilateral triangle
class CLG
{
// Function to find the side
// of the hexagon
 static float hexagonside(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    float x = a / 3;
    return x;
}
 
// Driver code
public static void main(String[] args)
{
    float a = 6;
    System.out.println(hexagonside(a));
     
}
}

Python3




# Python3 program to find the side of the
# largest hexagon which can be inscribed
# within an eqilateral triangle
 
# function to find the side of the hexagon
def hexagonside(a):
     
    # Side cannot be negative
    if a < 0:
        return -1
         
    # Side of the hexagon
    x = a // 3
    return x
 
# Driver code
a = 6
print(hexagonside(a))
 
# This code is contributed
# by Mohit kumar 29

C#




using System;
// C# program to find the side of the
// largest hexagon which can be inscribed
// within an equilateral triangle
class CLG
{
// Function to find the side
// of the hexagon
 static float hexagonside(float a)
{
  
    // Side cannot be negative
    if (a < 0)
        return -1;
  
    // Side of the hexagon
    float x = a / 3;
    return x;
}
  
// Driver code
public static void Main()
{
    float a = 6;
    Console.Write(hexagonside(a));
      
}
}

PHP




<?php
// PHP program to find the side of the
// largest hexagon which can be inscribed
// within an equilateral triangle
 
// Function to find the side
// of the hexagon
function hexagonside($a)
{
 
    // Side cannot be negative
    if ($a < 0)
        return -1;
 
    // Side of the hexagon
    $x = $a / 3;
    return $x;
}
 
// Driver code
$a = 6;
echo hexagonside($a) ;
     
// This code is contributed by Ryuga
?>

Javascript




<script>
 
// javascript program to find the side of the
// largest hexagon which can be inscribed
// within an equilateral triangle
 
// Function to find the side
// of the hexagon
 function hexagonside(a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    var x = a / 3;
    return x;
}
 
// Driver code
 
var a = 6;
document.write(hexagonside(a));
 
 
// This code contributed by Princi Singh
 
</script>

Output: 

2

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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