# 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++

`// CPP 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; ` `} ` |

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## 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)); ` ` ` ` ` `} ` `} ` |

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## 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)) ` |

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## 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) ` |

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## 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 ` `?> ` |

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**Output:**

Maximum Area = 90

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