Area of Reuleaux Triangle

Given an integer h which is the side of an equilateral triangle formed by the same vertices as the Reuleaux triangle, the task is to find and print the area of the Reuleaux triangle. 

Examples:

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

Approach: The shape made by the intersection of the three circles ABC is the Reuleaux Triangle and the triangle formed by the same vertices i.e. ABC is an equilateral triangle with side h. 

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

Below is the implementation of the above approach: 

C++

// C++ Program to find the area
// of Reuleaux triangle
#include <bits/stdc++.h>
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

PHP

<?php
// PHP 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
    $A = 0.70477 * pow($a, 2);
    return $A;
}

// Driver code
$a = 6;
echo ReuleauxArea($a);

// This code is contributed
// by Akanksha Rai

Javascript

<script>
// 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
</script>

Output:

25.3717

Time Complexity: O(1)

Auxiliary Space: O(1)