Elipse más grande que se puede inscribir dentro de un rectángulo que a su vez está inscrito dentro de un semicírculo

Aquí se da un semicírculo de radio r , que inscribe un rectángulo que a su vez inscribe una elipse. La tarea es encontrar el área de esta elipse más grande.
Ejemplos: 
 

Input: r = 5
Output: 19.625

Input: r = 11
Output: 94.985

Enfoque : 
 

1. Sea el largo del rectángulo = l y el ancho del rectángulo = b
2. Sea, la longitud del eje mayor de la elipse = 2x y la longitud del eje menor de la elipse = 2y
3. Como sabemos, el largo y el ancho del rectángulo más grande dentro de un semicírculo son r/√2 y √2r (consulte aquí)
4. Además, Área de la elipse dentro del rectángulo = (π*l*b)/4 = (πr^2/4)

A continuación se muestra la implementación del enfoque anterior : 
 

// C++ Program to find the biggest ellipse
// which can be inscribed within a rectangle
// which in turn is inscribed within a semicircle
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of the biggest ellipse
float ellipsearea(float r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the ellipse
    float a = (3.14 * r * r) / 4;
 
    return a;
}
 
// Driver code
int main()
{
    float r = 5;
    cout << ellipsearea(r) << endl;
    return 0;
}

// Java Program to find the biggest ellipse
// which can be inscribed within a rectangle
// which in turn is inscribed within a semicircle
class GFG
{
 
// Function to find the area
// of the biggest ellipse
static float ellipsearea(float r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the ellipse
    float a = (float)((3.14f * r * r) / 4);
 
    return a;
}
 
// Driver code
public static void main(String[] args)
{
    float r = 5;
    System.out.println(ellipsearea(r));
}
}
 
// This code is contributed by Code_Mech.

# Python3 Program to find the biggest ellipse
# which can be inscribed within a rectangle
# which in turn is inscribed within a semicircle
 
# Function to find the area of
# the biggest ellipse
def ellipsearea(r) :
 
    # the radius cannot be negative
    if (r < 0) :
        return -1;
 
    # area of the ellipse
    a = (3.14 * r * r) / 4;
 
    return a;
 
# Driver code
if __name__ == "__main__" :
 
    r = 5;
    print(ellipsearea(r));
 
# This code is contributed by Ryuga

// C# Program to find the biggest ellipse
// which can be inscribed within a rectangle
// which in turn is inscribed within a semicircle
using System;
class GFG
{
 
// Function to find the area
// of the biggest ellipse
static float ellipsearea(float r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the ellipse
    float a = (float)((3.14 * r * r) / 4);
 
    return a;
}
 
// Driver code
public static void Main()
{
    float r = 5;
    Console.WriteLine(ellipsearea(r));
}
}
 
// This code is contributed by Akanksha Rai

<?php
// PHP Program to find the biggest ellipse
// which can be inscribed within a rectangle
// which in turn is inscribed within a semicircle
 
// Function to find the area
// of the biggest ellipse
function ellipsearea($r)
{
 
    // the radius cannot be negative
    if ($r < 0)
        return -1;
 
    // area of the ellipse
    $a = (3.14 * $r * $r) / 4;
 
    return $a;
}
 
// Driver code
$r = 5;
echo ellipsearea($r) . "\n";
 
// This code is contributed by Akanksha Rai
?>

<script>
 
// javascript Program to find the biggest ellipse
// which can be inscribed within a rectangle
// which in turn is inscribed within a semicircle
 
 
// Function to find the area
// of the biggest ellipse
function ellipsearea(r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the ellipse
    var a = ((3.14 * r * r) / 4);
 
    return a;
}
 
// Driver code
var r = 5;
document.write(ellipsearea(r));
 
 
// This code is contributed by Amit Katiyar
 
</script>

19.625

Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)