Skip to content
Related Articles

Related Articles

Improve Article
Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
  • Last Updated : 18 Mar, 2021

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

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live




My Personal Notes arrow_drop_up
Recommended Articles
Page :