content: package v105;
  
  import java.io.BufferedReader;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.StringTokenizer;
  
  public class BoundingBox_UVa10577 {
  	
  	static final double EPS = 1e-9, INF = 1e9;
  	
  	public static void main(String[] args) throws IOException {
  		
  		Scanner sc = new Scanner(System.in);
  		PrintWriter out = new PrintWriter(System.out);
  	
  		int k = 1;
  		while(true)
  		{
  			int n = sc.nextInt();
  			if(n == 0) break;
  			Point p = new Point(sc.nextDouble(), sc.nextDouble());
  			Point q = new Point(sc.nextDouble(), sc.nextDouble());
  			Point r = new Point(sc.nextDouble(), sc.nextDouble());
  			
  			Point center = circumCircle(p, q, r);
  			
  			double theta = 2 * Math.PI / n, maxX, maxY, minX, minY;
  			maxX = minX = p.x;
  			maxY = minY = p.y;
  			
  			for(int i = 1; i < n; i++)
  			{
  				p = p.rotate(theta, center);
  				
  				maxX = Math.max(p.x, maxX);
  				minX = Math.min(p.x, minX);
  				maxY = Math.max(p.y, maxY);
  				minY = Math.min(p.y, minY);
  			}
  			
  			out.printf("Polygon %d: %.3f\n", k++, (maxX - minX) * (maxY - minY));
  		}
  		out.flush();
  	}
  	
  	static Point circumCircle(Point a, Point b, Point c) 
  	{
  		double bax = b.x - a.x, bay = b.y - a.y;
  		double cax = c.x - a.x, cay = c.y - a.y;
  
  		double e = bax * (a.x + b.x) + bay * (a.y + b.y);
  		double f = cax * (a.x + c.x) + cay * (a.y + c.y);
  		double g = 2.0 * (bax * (c.y - b.y) - bay * (c.x - b.x));
  
  		if (Math.abs(g) < EPS) return null;
  
  		return new Point((cay*e - bay*f) / g, (bax*f - cax*e) / g);
  
  	}
  
  	static class Point
  	{
  		double x, y;
  		
  		Point(double a, double b)
  		{
  			x = a; y = b;
  		}
  		
  		double dist(Point p)
  		{
  			return Math.sqrt((p.x - x) * (p.x - x) + (p.y - y) * (p.y - y));
  		}
  		
  		Point rotate(double theta) 
  		{
  			double c = Math.cos(theta), s = Math.sin(theta);
  			return new Point(x * c - y * s, x * s + y * c); 
  		}
  		
  		Point rotate(double theta, Point p)
  		{
  			Vector v = new Vector(p, new Point(0, 0));
  			return translate(v).rotate(theta).translate(v.reverse());
  		}
  		
  		Point translate(Vector v)
  		{
  			return new Point(x + v.x, y + v.y);
  		}
  	}
  	
  	static class Vector
  	{
  		double x, y;
  		
  		Vector(double a, double b)
  		{
  			x = a; y = b;
  		}
  		
  		Vector(Point p, Point q)
  		{
  			x = q.x - p.x; y = q.y - p.y;
  		}
  		
  		Vector reverse()
  		{
  			return new Vector(-x, -y);
  		}
  	}
  	
  	static class Scanner 
  	{
  		StringTokenizer st;
  		BufferedReader br;
  
  		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
  
  		public String next() throws IOException 
  		{
  			while (st == null || !st.hasMoreTokens()) 
  				st = new StringTokenizer(br.readLine());
  			return st.nextToken();
  		}
  
  		public int nextInt() throws IOException {return Integer.parseInt(next());}
  		
  		public long nextLong() throws IOException {return Long.parseLong(next());}
  
  		public String nextLine() throws IOException {return br.readLine();}
  		
  		public double nextDouble() throws IOException
  		{
  			String x = next();
  			StringBuilder sb = new StringBuilder("0");
  			double res = 0, f = 1;
  			boolean dec = false, neg = false;
  			int start = 0;
  			if(x.charAt(0) == '-')
  			{
  				neg = true;
  				start++;
  			}
  			for(int i = start; i < x.length(); i++)
  				if(x.charAt(i) == '.')
  				{
  					res = Long.parseLong(sb.toString());
  					sb = new StringBuilder("0");
  					dec = true;
  				}
  				else
  				{
  					sb.append(x.charAt(i));
  					if(dec)
  						f *= 10;
  				}
  			res += Long.parseLong(sb.toString()) / f;
  			return res * (neg?-1:1);
  		}
  		
  		public boolean ready() throws IOException {return br.ready();}
  
  
  	}
  }
  