Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon

Given a regular hexagon of side length a which inscribes a square which in turn inscribes a reuleaux triangle. The task is to find the maximum possible area of this reuleaux triangle.
Examples:

Input: a = 5
Output: 28.3287

Input: a = 9
Output: 91.7848

Approach: As the side of the square inscribed within a hexagon is x = 1.268a. Please refer Largest Square that can be inscribed within a hexagon.
Also, in the reuleaux triangle, h = x = 1.268a. 
So, Area of the reuleaux triangle, A = 0.70477*h^2 = 0.70477*(1.268a)^2.
Below is the implementation of the above approach: 

C++

// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within a hexagon
#include <bits/stdc++.h>
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

PHP

<?php
// PHP 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
    $h = 1.268 * $a;

    // area of the reuleaux triangle
    $A = 0.70477 * pow($h, 2);

    return $A;
}

// Driver code
$a = 5;
echo round(Area($a), 4);

// This code is contributed by Ryuga
?>

Javascript

<script>

// 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

</script>

Output:

28.3287

Time complexity: O(1)

Auxiliary Space: O(1)