菱形内切圆的面积

给定一个对角线为a和b的菱形，其中包含一个内切圆。任务是根据 a 和 b 找到该圆的面积。
例子：

Input: l = 5, b = 6
Output: 11.582

Input: l = 8, b = 10
Output: 30.6341

处理方法：从图中可以看出，内切圆的半径也是直角三角形AOB的高h=OH 。为了找到它，我们使用三角形面积方程：

Area AOB = 1/2 * (a/2) * (b/2) = ab/8 = 12ch

其中c = AB即斜边。所以，

r = h = ab/4c = ab/4√(a^2/4 + b^2/4) = ab/2√(a^2+b^2)

因此圆的面积是

A = Π * r^2 = Π a^2 b^2 /4(a2 + b2)

下面是上述方法的实现：

C++

// C++ Program to find the area of the circle
// which can be inscribed within the rhombus
#include 
using namespace std;
 
// Function to find the area
// of the inscribed circle
float circlearea(float a, float b)
{
 
    // the diagonals cannot be negative
    if (a < 0 || b < 0)
        return -1;
 
    // area of the circle
    float A = (3.14 * pow(a, 2) * pow(b, 2))
            / (4 * (pow(a, 2) + pow(b, 2)));
    return A;
}
 
// Driver code
int main()
{
    float a = 8, b = 10;
    cout << circlearea(a, b) << endl;
 
    return 0;
}

Java

// Java Program to find the area of the circle
// which can be inscribed within the rhombus
 
public class GFG {
     
    // Function to find the area
    // of the inscribed circle
    public static float circlearea(double a, double b)
    {
        // the diagonals cannot be negative
        if (a < 0 || b < 0)
            return -1 ;
         
        //area of the circle
        float A = (float) ((3.14 * Math.pow(a, 2) * Math.pow(b, 2))
                        / (4 * (Math.pow(a, 2) + Math.pow(b, 2)))) ;
         
        return A ;
    }
 
    // Driver code
    public static void main(String[] args) {
        float a = 8, b = 10 ;
         
        System.out.println(circlearea(a, b));
 
    }
// This code is contributed by ANKITRAI1
}

Python 3

# Python 3 Program to find the area of the circle
# which can be inscribed within the rhombus
 
 
# Function to find the area
# of the inscribed circle
def circlearea(a, b):
 
    # the diagonals cannot be negative
    if (a < 0 or b < 0):
        return -1
 
    # area of the circle
    A = ((3.14 * pow(a, 2) * pow(b, 2))/
        (4 * (pow(a, 2) + pow(b, 2))))
    return A
 
# Driver code
if __name__ == "__main__":
    a = 8
    b = 10
    print( circlearea(a, b))
 
# This code is contributed by ChitraNayal

C#

// C# Program to find the area of the circle
// which can be inscribed within the rhombus
using System;
 
public class GFG {
     
    // Function to find the area
    // of the inscribed circle
    public static float circlearea(double a, double b)
    {
        // the diagonals cannot be negative
        if (a < 0 || b < 0)
            return -1 ;
         
        //area of the circle
        float A = (float) ((3.14 * Math.Pow(a, 2) * Math.Pow(b, 2))
                        / (4 * (Math.Pow(a, 2) + Math.Pow(b, 2)))) ;
         
        return A ;
    }
 
    // Driver code
    public static void Main() {
        float a = 8, b = 10 ;
         
        Console.WriteLine(circlearea(a, b));
 
    }
// This code is contributed by inder_verma..
}

Javascript

 
// javascript Program to find the area of the circle
// which can be inscribed within the rhombus
 
     
// Function to find the area
// of the inscribed circle
function circlearea(a , b)
{
    // the diagonals cannot be negative
    if (a < 0 || b < 0)
        return -1 ;
     
    //area of the circle
    var A =  ((3.14 * Math.pow(a, 2) * Math.pow(b, 2))
                    / (4 * (Math.pow(a, 2) + Math.pow(b, 2)))) ;
     
    return A ;
}
 
// Driver code
 
var a = 8, b = 10 ;
 
document.write(circlearea(a, b).toFixed(4));
 
 
// This code is contributed by Amit Katiyar
 

输出：

30.6341