# 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; ` `} ` |

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

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## 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 ` |

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## 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 ` |

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## 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 ` `?> ` |

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**Output:**

10

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