# Maximum area of rectangle possible with given perimeter

Given the perimeter of a rectangle, the task is to find the maximum area of a rectangle which can use n-unit length as its perimeter.

**Note:** Length and Breadth must be an integral value.

**Example:**

Input:perimeter = 15Output:Maximum Area = 12Input:perimeter = 16Output:Maximum Area = 16

**Approach:** For area to be maximum of any rectangle the difference of length and breadth must be minimal. So, in such case the length must be ceil (perimeter / 4) and breadth will be be floor(perimeter /4). Hence the maximum area of a rectangle with given perimeter is equal to **ceil(perimeter/4) * floor(perimeter/4)**.

Below is the implementation of the above approach:

## C++

`// C++ to find maximum area rectangle` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find max area` `int` `maxArea(` `float` `perimeter)` `{` ` ` `int` `length = (` `int` `)` `ceil` `(perimeter / 4);` ` ` `int` `breadth = (` `int` `)` `floor` `(perimeter / 4);` ` ` `// return area` ` ` `return` `length * breadth;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `n = 38;` ` ` `cout << ` `"Maximum Area = "` `<< maxArea(n);` ` ` `return` `0;` `}` |

## Java

`//Java to find maximum area rectangle` `import` `java.io.*;` `class` `GFG {` `// Function to find max area` `static` `int` `maxArea(` `float` `perimeter)` `{` ` ` `int` `length = (` `int` `)Math.ceil(perimeter / ` `4` `);` ` ` `int` `breadth = (` `int` `)Math.floor(perimeter / ` `4` `);` `// return area` `return` `length * breadth;` `}` `// Driver code` ` ` ` ` `public` `static` `void` `main (String[] args) {` ` ` `float` `n = ` `38` `;` ` ` `System.out.println(` `"Maximum Area = "` `+` ` ` `maxArea(n));` ` ` ` ` `}` `}` |

## Python3

`# Python3 program to find` `# maximum area rectangle` `from` `math ` `import` `ceil, floor` `# Function to find max area` `def` `maxArea(perimeter):` ` ` `length ` `=` `int` `(ceil(perimeter ` `/` `4` `))` ` ` `breadth ` `=` `int` `(floor(perimeter ` `/` `4` `))` ` ` `# return area` ` ` `return` `length ` `*` `breadth` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `n ` `=` `38` ` ` `print` `(` `"Maximum Area ="` `, maxArea(n))` |

## C#

`// C# to find maximum area rectangle` `using` `System;` `class` `GFG` `{` `// Function to find max area` `static` `int` `maxArea(` `float` `perimeter)` `{` ` ` `int` `length = (` `int` `)Math.Ceiling(perimeter / 4);` ` ` `int` `breadth = (` `int` `)Math.Floor(perimeter / 4);` ` ` `// return area` ` ` `return` `length * breadth;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `float` `n = 38;` ` ` `Console.WriteLine(` `"Maximum Area = "` `+` ` ` `maxArea(n));` `}` `}` `// This code is contributed` `// by Akanksha Rai(Abby_akku)` |

## PHP

`<?php` `// PHP to find maximum area rectangle` `// Function to find max area` `function` `maxArea(` `$perimeter` `)` `{` ` ` `$length` `= (int)` `ceil` `(` `$perimeter` `/ 4);` ` ` `$breadth` `= (int)` `floor` `(` `$perimeter` `/ 4);` ` ` `// return area` ` ` `return` `(` `$length` `* ` `$breadth` `);` `}` `// Driver code` `$n` `= 38;` `echo` `"Maximum Area = "` `, maxArea(` `$n` `);` `// This code is contributed by jit_t` `?>` |

## Javascript

`<script>` `// JavaScript to find maximum area rectangle` `// Function to find max area` `function` `maxArea(perimeter)` `{` ` ` `let length = Math.ceil(perimeter / 4);` ` ` `let breadth = Math.floor(perimeter / 4);` ` ` `// return area` ` ` `return` `length * breadth;` `}` `// Driver code` `let n = 38;` `document.write(` `"Maximum Area = "` `+ maxArea(n));` `// This code is contributed by Manoj.` `</script>` |

**Output:**

Maximum Area = 90

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

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