等边三角形内接矩形的最大面积

给定一个整数A ，它表示等边三角形的边，任务是找到可以内接在三角形中的矩形的最大面积。
例子：

Input: A = 10 
Output: 21.65 
Explanation: 
Maximum area of rectangle inscribed in an equilateral triangle of side 10 is 21.65.
Input: A = 12 
Output: 31.176 
Explanation: 
Maximum area of rectangle inscribed in an equilateral triangle of side 12 is 31.176. 
 

方法：这个想法是利用等边三角形的内角是 60 ^o的事实。然后，从三角形的边之一绘制垂线并借助以下公式计算矩形的边

The length of Rectangle = (Side of Equilateral Triangle)/2
The breadth of Rectangle = sqrt(3) * (Side of Equilateral Triangle)/4 
 

然后，矩形的最大面积将是$\sqrt 3 * \frac {A^2}{8}$
下面是上述方法的实现：

C++

// CPP implementation to find the
// maximum area inscribed in an
// equilateral triangle
#include
using namespace std;
 
// Function to find the maximum area
// of the rectangle inscribed in an
// equilateral triangle of side S
double solve(int s)
{
    // Maximum area of the rectangle
    // inscribed in an equilateral
    // triangle of side S
    double area = (1.732 * pow(s, 2))/8;
    return area;
     
}
     
// Driver Code
int main()
{
    int n = 14;
    cout << solve(n);
}
     
// This code is contributed by Surendra_Gangwar

Java

// Java implementation to find the
// maximum area inscribed in an
// equilateral triangle
 
class GFG
{
    // Function to find the maximum area
    // of the rectangle inscribed in an
    // equilateral triangle of side S
    static double solve(int s)
    {
        // Maximum area of the rectangle
        // inscribed in an equilateral
        // triangle of side S
        double area = (1.732 * Math.pow(s, 2))/8;
        return area;
     
    }
     
    // Driver Code
    public static void  main(String[] args)
    {
        int n = 14;
        System.out.println(solve(n));
    }
}
     
// This article is contributed by Apurva raj

Python3

# Python3 implementation to find the
# maximum area inscribed in an
# equilateral triangle
 
# Function to find the maximum area
# of the rectangle inscribed in an
# equilateral triangle of side S
def solve(s):
     
    # Maximum area of the rectangle
    # inscribed in an equilateral
    # triangle of side S
    area = (1.732 * s**2)/8
    return area
     
     
# Driver Code
if __name__=='__main__':
    n = 14
    print(solve(n))

C#

// C# implementation to find the
// maximum area inscribed in an
// equilateral triangle
using System;
 
class GFG
{
    // Function to find the maximum area
    // of the rectangle inscribed in an
    // equilateral triangle of side S
    static double solve(int s)
    {
        // Maximum area of the rectangle
        // inscribed in an equilateral
        // triangle of side S
        double area = (1.732 * Math.Pow(s, 2))/8;
        return area;
      
    }
      
    // Driver Code
    public static void  Main(String[] args)
    {
        int n = 14;
        Console.WriteLine(solve(n));
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

 
// Javascript implementation to find the
// maximum area inscribed in an
// equilateral triangle
 
// Function to find the maximum area
// of the rectangle inscribed in an
// equilateral triangle of side S
function solve(s)
{
 
    // Maximum area of the rectangle
    // inscribed in an equilateral
    // triangle of side S
    let area = (1.732 * Math.pow(s, 2))/8;
    return area;
     
}
     
// Driver Code
    let n = 14;
    document.write(solve(n));
 
// This code is contributed by Manoj
 

输出：

42.434

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