# Area of the biggest ellipse inscribed within a rectangle

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
``` ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

Output:

```11.775
```

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