可以内切在等边三角形内的六边形上的最大正方形

在此给出了边长为a的等边三角形，该三角形刻有六边形，而六角形又刻有正方形。任务是找到正方形的边长。
例子：

Input:  a = 6
Output: 2.538

Input: a = 8
Output: 3.384

方法：
我们知道，刻在等边三角形内的六边形的边长为h = a / 3 。请参考可刻在等边三角形内的最大六角形。
另外，可以在六边形内刻入的正方形的边长为x = 1.268h。请参考可以在六边形内刻入的最大正方形。
因此，内接在六边形内的正方形的边长又接在等边三角形内， x = 0.423a 。
下面是上述方法的实现：

C++

// C++ program to find the side of the largest square
// that can be inscribed within the hexagon which in return
// is incsribed within an equilateral triangle
#include 
using namespace std;
 
// Function to find the side
// of the square
float squareSide(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    float x = 0.423 * a;
    return x;
}
 
// Driver code
int main()
{
    float a = 8;
    cout << squareSide(a) << endl;
 
    return 0;
}

Java

// Java program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
class cfg
{
     
// Function to find the side
// of the square
static float squareSide(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    float x = (0.423f * a);
    return x;
}
 
// Driver code
public static void main(String[] args)
{
    float a = 8;
    System.out.println(squareSide(a));
 
}
}
 
// This code is contributed by
// Mukul Singh.

Python3

# Python 3 program to find the side of the
# largest square that can be inscribed
# within the hexagon which in return
# is incsribed within an equilateral triangle
 
# Function to find the side of the square
def squareSide(a):
     
    # Side cannot be negative
    if (a < 0):
        return -1
 
    # side of the square
    x = 0.423 * a
    return x
 
# Driver code
if __name__ == '__main__':
    a = 8
    print(squareSide(a))
 
# This code is contributed by
# Sanjit_Prasad

C#

// C# program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
using System;
 
class GFG
{
     
// Function to find the side
// of the square
static float squareSide(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    float x = (0.423f * a);
    return x;
}
 
// Driver code
public static void Main()
{
    float a = 8;
    Console.WriteLine(squareSide(a));
}
}
 
// This code is contributed by
// shs

Javascript

// javascript program to find the side of the
// largest square that can be inscribed
// within the hexagon which in return is
// incsribed within an equilateral triangle
 
// Function to find the side
// of the square
function squareSide(a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // side of the square
    var x = (0.423 * a);
    return x;
}
 
// Driver code
var a = 8;
document.write(squareSide(a));
 
// This code is contributed by Princi Singh

输出：

3.384