Minimum area of a Polygon with three points given

// C# program to find minimum 
// area of polygon of number of 
// sides more than three with 
// given three points.  
using System;
using System.Collections.Generic;

class GFG 
{
    
    // Assigning pi value to variable 
    static double pi = 3.14159265359; 
           
    static double fmod(double a, double b) 
    {
      int result = (int) Math.Floor(a / b);
      return a - result * b;
    }
         
    // calculating gcd value of 
    // two double values . 
    static double gcd(double x, double y) 
    { 
      return Math.Abs(y) < 1e-4 ? x : gcd(y, fmod(x, y)); 
    } 
           
    // Calculating minimum area of polygon through this function . 
    static double min_area_of_polygon(double Ax, double Ay, 
                                             double Bx, double By, 
                                             double Cx, double Cy) 
    { 
      double a, b, c, Radius, Angle_A, Angle_B, Angle_C,  
             semiperimeter, n, area; 
     
      // Calculating the length of the sides 
      // of the triangle formed from given 
      /// points a, b, c represents the  
      // length of different sides of triangle . 
      a = Math.Sqrt((Bx - Cx) * (Bx - Cx) + 
                    (By - Cy) * (By - Cy)); 
      b = Math.Sqrt((Ax - Cx) * (Ax - Cx) + 
                    (Ay - Cy) * (Ay - Cy)); 
      c = Math.Sqrt((Ax - Bx) * (Ax - Bx) + 
                    (Ay - By) * (Ay - By)); 
     
      // Here we have calculated the 
      // semiperimeter of a triangle . 
      semiperimeter = (a + b + c) / 2; 
     
      // Now from the semiperimeter area 
      // of triangle is derived 
      // through the heron's formula . 
      double area_triangle = Math.Sqrt(semiperimeter * 
                                      (semiperimeter - a) * 
                                      (semiperimeter - b) * 
                                      (semiperimeter - c)); 
     
      // Thus circumradius of the triangle 
      // is derived from the sides and 
      // area of the triangle calculated . 
      Radius = (a * b * c) / (4 * area_triangle); 
     
      // Now each angle of the triangle 
      // is derived from the sides 
      // of the triangle . 
      Angle_A = Math.Acos((b * b + c * c - a * a) / 
                          (2 * b * c)); 
      Angle_B = Math.Acos((a * a + c * c - b * b) / 
                          (2 * a * c)); 
      Angle_C = Math.Acos((b * b + a * a - c * c) / 
                          (2 * b * a)); 
     
      // Now n is calculated such that 
      // area is minimum for the regular n-gon . 
      n = pi / gcd(gcd(Angle_A, Angle_B), Angle_C); 
     
      // calculating area of regular n-gon 
      // through the circumradius of the triangle . 
      area = (n * Radius * Radius * 
              Math.Sin((2 * pi) / n)) / 2; 
     
      return area; 
    }   
  
  // Driver code
  static void Main() 
  {
      // Three points are given as input . 
      double Ax, Ay, Bx, By, Cx, Cy; 
      Ax = 0.00; 
      Ay = 0.00; 
      Bx = 1.00; 
      By = 1.00; 
      Cx = 0.00; 
      Cy = 1.00; 
      Console.WriteLine(String.Format("{0:0.00}", min_area_of_polygon(Ax, Ay, 
                                             Bx, By, 
                                             Cx, Cy)));
  }
}

// This code is contributed by divyeshrabadiya07