可以在正方形内切出的最大六边形

给定正方形a的边，任务是找到可以在给定正方形内切入的最大六边形的边。
例子：

Input: a = 6 
Output: 3.1056
Input: a = 8 
Output: 4.1408 
 

方法：：假设六边形的边为x并假设正方形的边a被划分为较小的长度b和较大的长度c，即a = b + c
现在从图中我们看到，

b² + b² = x² which gives b = x / √2 
Now again, d / (2 * x) = cos(30) = √3 / 2 i.e. d = x√3 
And, c² + c² = d² which gives c = d / √2 = x√3 / √2 
Since, a = b + c. So, a = x / √2 + x√3 / √2 = ((1 + √3) / √2) * x = 1.932 * x 
So, side of the hexagon, x = 0.5176 * a 
 

下面是上述方法的实现：

C++

// C++ Program to find the biggest hexagon which
// can be inscribed within the given square
#include 
using namespace std;
 
// Function to return the side
// of the hexagon
float hexagonside(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    float x = 0.5176 * a;
    return x;
}
 
// Driver code
int main()
{
    float a = 6;
    cout << hexagonside(a) << endl;
    return 0;
}

Java

// Java  Program to find the biggest hexagon which
// can be inscribed within the given square
 
import java.io.*;
 
class GFG {
     
// Function to return the side
// of the hexagon
static double hexagonside(double a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    double x = (0.5176 * a);
    return x;
}
 
// Driver code
    public static void main (String[] args) {
 
        double a = 6;
        System.out.println (hexagonside(a));
    }
//This code is contributed by ajit.   
}

Python 3

# Python 3 Program to find the biggest
# hexagon which can be inscribed within
# the given square
 
# Function to return the side
# of the hexagon
def hexagonside(a):
 
    # Side cannot be negative
    if (a < 0):
        return -1;
 
    # Side of the hexagon
    x = 0.5176 * a;
    return x;
 
# Driver code
a = 6;
print(hexagonside(a));
 
# This code is contributed
# by Akanksha Rai

C#

// C# Program to find the biggest hexagon which
// can be inscribed within the given square
using System;
 
class GFG
{
         
// Function to return the side
// of the hexagon
static double hexagonside(double a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    double x = (0.5176 * a);
    return x;
}
 
// Driver code
public static void Main ()
{
    double a = 6;
    Console.WriteLine(hexagonside(a));
}
}
 
// This code is contributed by Ryuga.

Javascript

 
// Javascript Program to find the biggest hexagon which
// can be inscribed within the given square
 
// Function to return the side
// of the hexagon
function hexagonside(a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Side of the hexagon
    let x = 0.5176 * a;
    return x;
}
 
// Driver code
 
    let a = 6;
    document.write(hexagonside(a) + "<br>");
     
// This code is contributed by Manoj
 

输出：

3.1056