计算等边三角形圆的面积和周长的程序

给定等边三角形的边长，任务是找到给定等边三角形的圆的面积和周长。

例子：

Input: side = 6 
Output: Area = 9.4. Perimeter = 10.88

Input: side = 9
Output: Area = 21.21, Perimeter = 16.32

圆的属性为：

• 圆弧的中心与三角形的中心相同，即等边三角形的中值相交的点。
• 等边三角形的内接圆是通过等边三角形边缘的中点制成的。
• 等边三角形的圆的半径可以使用以下公式计算：

  $a / (\sqrt3 * 2)$ ，

  在哪里$a$是等边三角形边的长度。

• 下图显示了带有圆形的等边三角形：

  

• 方法：

  圆的面积= $\pi*r^2$和圆的周长= $2 * \pi * r$ ，其中r是给定圆的半径。

  同样是等边三角形的Incirce半径=(等边三角形的边)/ 3。
  所以，

  1. 用于使用“半径”计算“圆”面积的公式为：

     $\pi r^2 => ( \pi * a^2 ) / (3 * 2 )$

  2. 用于使用“半径”计算“圆”周长的公式为：

     $2 * \pi * r => 2 * \pi * (a/\sqrt3*2)$

     C

     // C program to find the area of Inscribed circle 
     // of equilateral triangle
     #include 
     #include 
     #define PI 3.14159265
       
     // function to find area of inscribed circle
     float area_inscribed(float a)
     {
         return (a * a * (PI / 12));
     }
       
     // function to find Perimeter of inscribed circle
     float perm_inscribed(float a)
     {
         return (PI * (a / sqrt(3)));
     }
       
     // Driver code
     int main()
     {
         float a = 6;
         printf("Area of inscribed circle is :%f\n",
                area_inscribed(a));
       
         printf("Perimeter of inscribed circle is :%f",
                perm_inscribed(a));
       
         return 0;
     }

     Java

     // Java code to find the area of inscribed
     // circle of equilateral triangle
     import java.lang.*;
       
     class GFG {
       
         static double PI = 3.14159265;
       
         // function to find the area of
         // inscribed circle
         public static double area_inscribed(double a)
         {
             return (a * a * (PI / 12));
         }
       
         // function to find the perimeter of
         // inscribed circle
         public static double perm_inscribed(double a)
         {
             return (PI * (a / Math.sqrt(3)));
         }
       
         // Driver code
         public static void main(String[] args)
         {
             double a = 6.0;
             System.out.println("Area of inscribed circle is :"
                                + area_inscribed(a));
       
             System.out.println("\nPerimeter of inscribed circle is :"
                                + perm_inscribed(a));
         }
     }

     Python3

     # Python3 code to find the area of inscribed 
     # circle of equilateral triangle
     import math
     PI = 3.14159265
           
     # Function to find the area of 
     # inscribed circle
     def area_inscribed(a):
         return (a * a * (PI / 12))
       
     # Function to find the perimeter of 
     # inscribed circle
     def perm_inscribed(a):
         return ( PI * (a / math.sqrt(3) ) )    
       
       
     # Driver code
     a = 6.0
     print("Area of inscribed circle is :% f"
                             % area_inscribed(a))
     print("\nPerimeter of inscribed circle is :% f"
                             % perm_inscribed(a))

     C#

     // C# code to find the area of
     // inscribed circle
     // of equilateral triangle
     using System;
       
     class GFG {
         static double PI = 3.14159265;
       
         // function to find the area of
         // inscribed circle
         public static double area_inscribed(double a)
         {
             return (a * a * (PI / 12));
         }
       
         // function to find the perimeter of
         // inscribed circle
         public static double perm_inscribed(double a)
         {
             return (PI * (a / Math.Sqrt(3)));
         }
       
         // Driver code
         public static void Main()
         {
             double a = 6.0;
             Console.Write("Area of inscribed circle is :"
                           + area_inscribed(a));
       
             Console.Write("\nPerimeter of inscribed circle is :"
                           + perm_inscribed(a));
         }
     }

     输出：

     Area of inscribed circle is :9.424778
     Perimeter of inscribed circle is :10.882796