#include<cstring>#include<cstdio>#include<iostream>#include<map>#include<algorithm>#include<cmath>using namespace std;const double INF=100000000;const double PI=acos(-1.0);int n;struct Point{ double x,y;}a,b,c,o,q;Point getOra(Point a,Point b,Point c){ double aa=2*(b.x-a.x); double bb=2*(b.y-a.y); double cc=b.x*b.x+b.y*b.y-a.x*a.x-a.y*a.y; double dd=2*(c.x-b.x); double ee=2*(c.y-b.y); double ff=c.x*c.x+c.y*c.y-b.x*b.x-b.y*b.y; Point ret; ret.x=(bb*ff-ee*cc)/(bb*dd-ee*aa); ret.y=(dd*cc-aa*ff)/(bb*dd-ee*aa); return ret;}int main(){ int Case=1; while(scanf("%d",&n)!=EOF) { if(n==0)return 0; scanf("%lf%lf",&a.x,&a.y); scanf("%lf%lf",&b.x,&b.y); scanf("%lf%lf",&c.x,&c.y); double co=cos(PI*2.0/(double)n); double si=sin(PI*2.0/(double)n); o=getOra(a,b,c); //printf("%lf %lfn",o.x,o.y); q.x=a.x-o.x; q.y=a.y-o.y; double hx,hy,lx,ly; hx=hy=-INF; lx=ly=INF; for(int i=0;i<=n;i++){ hx=max(hx,o.x+q.x); hy=max(hy,o.y+q.y); lx=min(lx,o.x+q.x); ly=min(ly,o.y+q.y); Point temp=q; q.x=temp.x*co-temp.y*si; q.y=temp.x*si+temp.y*co; } printf("Polygon %d: %.3lfn",Case++,(hy-ly)*(hx-lx)); } return 0;}
