Area of largest triangle that can be inscribed within a rectangle

Given a rectangle of length L and breadth B. 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++

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// 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

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// 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

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# 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#

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// 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

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<?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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Improved By : inderDuMCA, YatinGupta