N边正多边形的最大圆内切面积

给定一个边长为a的N边正多边形。任务是找到内接在多边形中的圆的面积。
注意：这个问题是This和This的混合版本
例子：

Input: N = 6, a = 4
Output: 37.6801
Explanataion:

In this, the polygon have 6 faces 
and as we see in fig.1 we clearly see 
that the angle  x  is 30 degree  
so the radius of circle will be ( a / (2  * tan(30))) 
Therefore, r = a√3/2

Input: N = 8, a = 8
Output: 292.81
Explanataion:

In this, the polygon have 8 faces 
and as we see in fig.2 we clearly see 
that the angle  x  is 22.5 degree  
so the radius of circle will be ( a / (2  * tan(22.5))) 
Therefore, r = a/0.828

方法：在上图中，我们看到多边形可以分成N个相等的三角形。查看其中一个三角形，我们看到中心处的整个角度可以分为 = 360/N
所以，角度x = 180/n
现在， tan(x) = (a / 2) * r
所以， r = a / ( 2 * tan(x))
所以，内切圆的面积是，

A = Πr² = Π * (a / (2 * tan(x))) * (a / (2*tan(x)))

下面是上述方法的实现：

C++

// C++ Program to find the area of a circle in
// inscribed in polygon
 
#include 
using namespace std;
 
// Function to find the area
// of a circle
float InscribedCircleArea(float n, float a)
{
    // Side and side length cannot be negative
    if (a < 0 && n < 0)
        return -1;
 
    // degree converted to radians
    float r = a / (2 * tan((180 / n) * 3.14159 / 180));
 
    // area of circle
    float Area = (3.14) * (r) * (r);
 
    return Area;
}
 
// Driver code
int main()
{
 
    // no.  of sides
    float n = 6;
 
    // side length
    float a = 4;
 
    cout << InscribedCircleArea(n, a) << endl;
 
    return 0;
}

Java

// Java Program to find the area of a circle
// inscribed in a polygon
import java.io.*;
 
class GFG {
 
    // Function to find the area
    // of a regular polygon
    static float InscribedCircleArea(float n, float a)
    {
        // Side and side length cannot be negative
        if (a < 0 && n < 0)
            return -1;
 
        // degree converted to radians
        float r = a / (float)(2 * Math.tan((180 / n) * 3.14159 / 180));
 
        // area of circle
        float Area = (float)(3.14) * (r) * (r);
 
        return Area;
    }
 
    // Driver code
 
    public static void main(String[] args)
    {
 
        // no.  of sides
        float n = 6;
 
        // side length
        float a = 4;
 
        System.out.println(InscribedCircleArea(n, a));
    }
}

Python3

# Python 3 Program to find the area
# of a circle inscribed
# in a polygon
from math import tan
 
# Function to find the area of a
# circle
def InscribedCircleArea(n, a):
    # Side and side length cannot
    # be negative
    if (a < 0 and n < 0):
        return -1
 
    # degree converted to radians
    r = a/(2 * tan((180 / n) * 3.14159 / 180));
 
    # area of circle
    Area = 3.14 * r * r
 
    return Area
 
# Driver code
if __name__ == '__main__':
    a = 4
    n = 6
 
    print('{0:.6}'.format(InscribedCircleArea(n, a)))
 
# This code is contributed by
# Chandan Agrawal

C#

// C# Program to find the area of a circle
// inscribed in a polygon
using System;
 
class GFG
{
 
// Function to find the area
// of a regular polygon
static float InscribedCircleArea(float n, float a)
{
    // Side and side length cannot be negative
    if (a < 0 && n < 0)
        return -1;
 
    // degree converted to radians
    float r = a / (float)(2 * Math.Tan((180 / n) *
                                 3.14159 / 180));
 
    // area of circle
    float Area = (float)(3.14) * (r) * (r);
 
    return Area;
}
 
// Driver code
public static void Main()
{
 
    // no. of sides
    float n = 6;
 
    // side length
    float a = 4;
 
    Console.WriteLine(InscribedCircleArea(n, a));
}
}
 
// This code is contributed by Ryuga

PHP

Javascript

输出：

37.6801