内接于正方形的最大Reuleaux三角形内接于六角形的正方形

给定边长为a的正六边形，该六边形刻有正方形，而该正方形又刻有reuleaux三角形。任务是找到该reuleaux三角形的最大可能面积。
例子：

Input: a = 5
Output: 28.3287

Input: a = 9
Output: 91.7848

方法：由于内切于六边形的正方形的边为x = 1.268a 。请参考可在六边形内刻出的最大正方形。
同样，在鲁洛三角形中， h = x = 1.268a 。
因此，鲁洛三角形的面积A = 0.70477 * h ^ 2 = 0.70477 *(1.268a)^ 2 。
下面是上述方法的实现：

C++

// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
#include 
using namespace std;
 
// Function to find the biggest reuleaux triangle
float Area(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    float h = 1.268 * a;
 
    // area of the reuleaux triangle
    float A = 0.70477 * pow(h, 2);
 
    return A;
}
 
// Driver code
int main()
{
    float a = 5;
    cout << Area(a) << endl;
 
    return 0;
}

Java

// Java Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
 
import java.io.*;
 
class GFG
{
 
// Function to find the biggest reuleaux triangle
static float Area(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    float h =(float) 1.268 * a;
 
    // area of the reuleaux triangle
    float A = (float)(0.70477 * Math.pow(h, 2));
 
    return A;
}
 
    // Driver code
    public static void main (String[] args)
    {
        float a = 5;
    System.out.println( Area(a));
    }
}
 
// This code is contributed by anuj_67

Python3

# Python3 Program to find the biggest
# Reuleaux triangle inscribed within
# in a square which in turn is
# inscribed within a hexagon
import math
 
# Function to find the biggest
# reuleaux triangle
def Area(a):
 
    # side cannot be negative
    if (a < 0):
        return -1
 
    # height of the reuleaux triangle
    h = 1.268 * a
 
    # area of the reuleaux triangle
    A = 0.70477 * math.pow(h, 2)
 
    return A
 
# Driver code
a = 5
print(Area(a),end = "\n")
 
# This code is contributed
# by Akanksha Rai

C#

// C# Program to find the biggest Reuleaux
// triangle inscribed within in a square
// which in turn is inscribed within a hexagon
using System;
 
class GFG
{
 
// Function to find the biggest reuleaux triangle
static float Area(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    float h =(float) 1.268 * a;
 
    // area of the reuleaux triangle
    float A = (float)(0.70477 * Math.Pow(h, 2));
 
    return A;
}
 
// Driver code
public static void Main ()
{
    float a = 5;
    Console.WriteLine(Area(a));
}
}
 
// This code is contributed
// by Akanksha Rai

Javascript

 
// Javascript Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
 
// Function to find the biggest reuleaux triangle
function Area(a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    let h = 1.268 * a;
 
    // area of the reuleaux triangle
    let A = 0.70477 * Math.pow(h, 2);
 
    return A;
}
 
// Driver code
    let a = 5;
    document.write(Area(a) + "<br>");
 
// This code is contributed by Mayank Tyagi
 

输出：

28.3287