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Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle

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  • Last Updated : 09 Jun, 2022

Given here is a semicircle of radius r, which inscribes a rectangle which in turn inscribes an ellipse. The task is to find the area of this largest ellipse.
Examples: 
 

Input: r = 5
Output: 19.625

Input: r = 11
Output: 94.985

 

Approach
 

  1. Let the, length of the rectangle = l and breadth of the rectangle = b
  2. Let, the length of the major axis of the ellipse = 2x and, the length of the minor axis of the ellipse = 2y
  3. As we know, length and breadth of the largest rectangle inside a semicircle are r/√2 and √2r(Please refer here)
  4. Also, Area of the ellipse within the rectangle = (π*l*b)/4 = (πr^2/4)

Below is the implementation of above approach
 

C++




// 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




// 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




# 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#




// 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
// 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
?>

Javascript




<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>

Output: 

19.625

 

Time Complexity: O(1)
Auxiliary Space: O(1)


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