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**=**(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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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. ` |

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## 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 ` `?> ` |

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**Output:**

11.775

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