# 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 = 3Output:11.775Input:7, b = 4Output: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**=**(Ï€ * x * y)**=**(Ï€ * 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)