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Area of the biggest ellipse inscribed within a rectangle

  • Last Updated : 18 Mar, 2021

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
 



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

 

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