# Area of largest triangle that can be inscribed within a rectangle

Given a rectangle of length and breadth . The task is to find the area of the biggest triangle that can be inscribed in it.**Examples**:

Input: L = 5, B = 4 Output: 10 Input: L = 3, B = 2 Output: 3

From the figure, it is clear that the largest triangle that can be inscribed in the rectangle, should stand on the same base & has height raising between the same parallel sides of the rectangle.

So, the base of the triangle = **B**

Height of the triangle = **L**

Therefore Area,

A = (L*B)/2

**Note**: It should also be clear that if base of the triangle = diagonal of rectangle, still the area of triangle so obtained = **lb/2** as diagonal of a rectangle divides it into 2 triangles of equal area.

Below is the implementation of the above approach:

## C++

`// C++ Program to find the biggest triangle` `// which can be inscribed within the rectangle` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the area` `// of the triangle` `float` `trianglearea(` `float` `l, ` `float` `b)` `{` ` ` `// a and b cannot be negative` ` ` `if` `(l < 0 || b < 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `float` `area = (l * b) / 2;` ` ` `return` `area;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `l = 5, b = 4;` ` ` `cout << trianglearea(l, b) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java Program to find the biggest triangle` `// which can be inscribed within the rectangle` `import` `java.util.*;` `class` `GFG` `{` ` ` `// Function to find the area` ` ` `// of the triangle` ` ` `static` `float` `trianglearea(` `float` `l, ` `float` `b)` ` ` `{` ` ` ` ` `// a and b cannot be negative` ` ` `if` `(l < ` `0` `|| b < ` `0` `)` ` ` `return` `-` `1` `;` ` ` ` ` `// area of the triangle` ` ` `float` `area = (l * b) / ` `2` `;` ` ` `return` `area;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `float` `l = ` `5` `, b = ` `4` `;` ` ` ` ` `System.out.println(trianglearea(l, b));` ` ` `}` `}` |

## Python3

`# Python3 Program to find the` `# biggest triangle which can be` `# inscribed within the rectangle` `# Function to find the area` `# of the triangle` `def` `trianglearea(l, b) :` ` ` `# a and b cannot be negative` ` ` `if` `(l < ` `0` `or` `b < ` `0` `) :` ` ` `return` `-` `1` ` ` `# area of the triangle` ` ` `area ` `=` `(l ` `*` `b) ` `/` `2` ` ` `return` `area` `# Driver code` `l ` `=` `5` `b ` `=` `4` `print` `(trianglearea(l, b))` `# This code is contributed` `# by Yatin Gupta` |

## C#

`// C# Program to find the biggest` `// triangle which can be inscribed` `// within the rectangle` `using` `System;` `class` `GFG` `{` `// Function to find the area` `// of the triangle` `static` `float` `trianglearea(` `float` `l,` ` ` `float` `b)` `{` ` ` `// a and b cannot be negative` ` ` `if` `(l < 0 || b < 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `float` `area = (l * b) / 2;` ` ` `return` `area;` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `float` `l = 5, b = 4;` ` ` ` ` `Console.WriteLine(trianglearea(l, b));` `}` `}` `// This code is contributed` `// by inder_verma` |

## PHP

`<?php` `// PHP Program to find the biggest` `// triangle which can be inscribed` `// within the rectangle` `// Function to find the area` `// of the triangle` `function` `trianglearea(` `$l` `, ` `$b` `)` `{` ` ` `// a and b cannot be negative` ` ` `if` `(` `$l` `< 0 ` `or` `$b` `< 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `$area` `= (` `$l` `* ` `$b` `) / 2;` ` ` `return` `$area` `;` `}` `// Driver code` `$l` `= 5; ` `$b` `= 4;` `echo` `trianglearea(` `$l` `, ` `$b` `);` `// This code is contributed` `// by inder_verma` `?>` |

## Javascript

`<script>` `// javascript Program to find the biggest triangle` `// which can be inscribed within the rectangle` `// Function to find the area` `// of the triangle` `function` `trianglearea( l, b)` `{` ` ` `// a and b cannot be negative` ` ` `if` `(l < 0 || b < 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `let area = (l * b) / 2;` ` ` `return` `area;` `}` `// Driver code` ` ` `let l = 5, b = 4;` ` ` `document.write( trianglearea(l, b) );` `// This code contributed by aashish1995` `</script>` |

**Output:**

10