长方形内接三角形的最大面积

给定一个长矩形$L$和广度$B$ .任务是找到可以内切的最大三角形的面积。
例子：

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

Input: L = 3, B = 2
Output: 3

从图中可以清楚地看出，矩形内可以内切的最大三角形，应该在同一个底上，并且在矩形的相同平行边之间具有升高的高度。
所以，三角形的底= B
三角形的高度 = L
因此面积，

A = (L*B)/2

注意：还应该清楚的是，如果三角形的底边 = 矩形的对角线，仍然如此获得的三角形面积 = lb/2作为矩形的对角线将其分成 2 个等面积的三角形。
下面是上述方法的实现：

C++

// C++ Program to find the biggest triangle
// which can be inscribed within the rectangle
#include 
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

Javascript

 
// 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
 

输出：

10

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