鲁洛三角区

给定一个整数h ，它是由与鲁洛三角形相同的顶点形成的等边三角形的边，任务是找到并打印鲁洛三角形的面积。

例子：

Input: h = 6 
Output: 25.3717
Input: h = 9 
Output: 57.0864 
 

方法：三个圆ABC相交所形成的形状是鲁洛三角形，同一个顶点所形成的三角形即ABC是一个边为h的等边三角形。

Now, Area of sector ACB, A1 = (π * h²) / 6 
Similarly, Area of sector CBA, A2 = (π * h²) / 6 
And, Area of sector BAC, A3 = (π * h²) / 6 
So, A1 + A2 + A3 = (π * h²) / 2 
Since, the area of the triangle is added thrice in the sum. 
So, Area of the Reuleaux Triangle, A = (π * h²) / 2 – 2 * (Area of equilateral triangle) = (π – √3) * h² / 2 = 0.70477 * h² 
 

下面是上述方法的实现：

C++

// C++ Program to find the area
// of Reuleaux triangle
#include 
using namespace std;
 
// Function to find the Area
// of the Reuleaux triangle
float ReuleauxArea(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Area of the Reuleaux triangle
    float A = 0.70477 * pow(a, 2);
    return A;
}
 
// Driver code
int main()
{
    float a = 6;
    cout << ReuleauxArea(a) << endl;
    return 0;
}

Java

// Java Program to find the area
// of Reuleaux triangle
 
public class GFG
{
    // Function to find the Area
    // of the Reuleaux triangle
    static double ReuleauxArea(float a)
    {
     
        // Side cannot be negative
        if (a < 0)
            return -1;
     
        // Area of the Reuleaux triangle
        double A = (double)0.70477 * Math.pow(a, 2);
        return A;
    }
     
    // Driver code
    public static void main(String args[])
    {
        float a = 6;
        System.out.println(ReuleauxArea(a)) ;
    }
    // This code is contributed by Ryuga
}

Python3

# Python3 program to find the area
# of Reuleaux triangle
import math as mt
 
# function to the area of the
# Reuleaux triangle
def ReuleauxArea(a):
     
    # Side cannot be negative
    if a < 0:
        return -1
    # Area of the Reauleax triangle
    return 0.70477 * pow(a, 2)
 
# Driver code
a = 6
print(ReuleauxArea(a))
 
# This code is contributed
# by Mohit Kumar

C#

// C# Program to find the area 
// of Reuleaux triangle 
   
using System;
 
public class GFG
{
    // Function to find the Area 
    // of the Reuleaux triangle 
    static double ReuleauxArea(float a) 
    { 
       
        // Side cannot be negative 
        if (a < 0) 
            return -1; 
       
        // Area of the Reuleaux triangle 
        double A = (double)0.70477 * Math.Pow(a, 2); 
        return A; 
    } 
       
    // Driver code 
    public static void Main() 
    { 
        float a = 6; 
        Console.WriteLine(ReuleauxArea(a)) ; 
    }
}
    // This code is contributed by Subhadeep

---

Javascript

// javascript Program to find the area
// of Reuleaux triangle
 
// Function to find the Area
// of the Reuleaux triangle
function ReuleauxArea(a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Area of the Reuleaux triangle
    var A = 0.70477 * Math.pow(a, 2);
    return A;
}
 
// Driver code
   
var a = 6;
document.write(ReuleauxArea(a)) ;
 
// This code is contributed by Princi Singh

输出：

25.3717

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