Area of the biggest ellipse inscribed within a rectangle

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Given here is a rectangle of length l & breadth b, the task is to find the area of the biggest ellipse that can be inscribed within it.
Examples:

Input: l = 5, b = 3
Output: 11.775

Input: 7, b = 4
Output: 21.98

Approach:

Let, the length of the major axis of the ellipse = 2x and the length of the minor axis of the ellipse = 2y
From the diagram, it is very clear that,
2x = l
2y = b
So, Area of the ellipse = (? * x * y) = (? * l * b) / 4

Below is the implementation of the above approach:

C++

// C++ Program to find the biggest ellipse
// which can be inscribed within the rectangle
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of the ellipse
float ellipse(float l, float b)
{
 
    // The sides cannot be negative
    if (l < 0 || b < 0)
        return -1;
 
    // Area of the ellipse
    float x = (3.14 * l * b) / 4;
 
    return x;
}
 
// Driver code
int main()
{
    float l = 5, b = 3;
    cout << ellipse(l, b) << endl;
 
    return 0;
}

Java

// Java Program to find the biggest rectangle 
// which can be inscribed within the ellipse 
import java.util.*; 
import java.lang.*; 
import java.io.*; 
 
class GFG
{ 
     
// Function to find the area 
// of the rectangle 
static float ellipse(float l, float b) 
{ 
     
    // a and b cannot be negative 
    if (l < 0 || b < 0) 
        return -1; 
    float x = (float)(3.14 * l * b) / 4;
 
    return x; 
     
} 
     
// Driver code 
public static void main(String args[]) 
{ 
    float a = 5, b = 3; 
    System.out.println(ellipse(a, b)); 
} 
} 
 
// This code is contributed
// by Mohit Kumar

Python3

# Python3 Program to find the biggest ellipse 
# which can be inscribed within the rectangle 
 
# Function to find the area
# of the ellipse 
def ellipse(l, b): 
 
    # The sides cannot be negative 
    if l < 0 or b < 0: 
        return -1
 
    # Area of the ellipse 
    x = (3.14 * l * b) / 4
 
    return x 
 
# Driver code 
if __name__ == "__main__":
 
    l, b = 5, 3
    print(ellipse(l, b)) 
 
# This code is contributed 
# by Rituraj Jain

C#

// C# Program to find the biggest rectangle 
// which can be inscribed within the ellipse 
using System;
 
class GFG
{ 
     
// Function to find the area 
// of the rectangle 
static float ellipse(float l, float b) 
{ 
     
    // a and b cannot be negative 
    if (l < 0 || b < 0) 
        return -1; 
    float x = (float)(3.14 * l * b) / 4;
 
    return x; 
     
} 
     
// Driver code 
public static void Main() 
{ 
    float a = 5, b = 3; 
    Console.WriteLine(ellipse(a, b)); 
} 
} 
 
// This code is contributed
// by Code_Mech.

PHP

<?php
// PHP Program to find the biggest ellipse
// which can be inscribed within the rectangle
 
// Function to find the area
// of the ellipse
function ellipse($l, $b)
{
 
    // The sides cannot be negative
    if ($l < 0 || $b < 0)
        return -1;
 
    // Area of the ellipse
    $x = (3.14 * $l * $b) / 4;
 
    return $x;
}
 
// Driver code
$l = 5; $b = 3;
echo ellipse($l, $b) . "\n";
 
// This code is contributed
// by Akanksha Rai
?>

Javascript

<script>
 
// javascript Program to find the biggest rectangle 
// which can be inscribed within the ellipse 
  
 
// Function to find the area 
// of the rectangle 
function ellipse(l , b) 
{ 
     
    // a and b cannot be negative 
    if (l < 0 || b < 0) 
        return -1; 
    var x = (3.14 * l * b) / 4;
 
    return x; 
     
} 
     
// Driver code 
 
var a = 5, b = 3; 
document.write(ellipse(a, b)); 
 
 
// This code is contributed by Amit Katiyar 
 
</script>

Output:

11.775

Time Complexity: O(1)

Auxiliary Space: O(1)

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