Red Huang

//====================================================================||  
//                                                                    ||  
//                                                                    ||  
//                         Author : GCA                               ||  
//                  6AE7EE02212D47DAD26C32C0FE829006                  ||  
//====================================================================||  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
using namespace std;  
#ifdef ONLINE\_JUDGE  
#define ll "%lld"  
#else  
#define ll "%I64d"  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 55  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo INT\_MAX  
#define Set\_oo 0x3f  
#define Is\_debug true  
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)  
#define eps 1e-6  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
int n;  
int ff;  
double pi=acos(-1);  
struct point{  
    double x,y;  
}pt\[4\];  
inline double cosd(double a){  
    return cos(a\*pi/180);  
}  
inline double sind(double a){  
    return sin(a\*pi/180);  
}  
point cm(point a,point b,point c){  
    point ua,ub,va,vb,ans;  
    ua.x=(a.x+b.x)/2;  
    ua.y=(a.y+b.y)/2;  
    ub.x=ua.x-a.y+b.y;  
    ub.y=ua.y+a.x-b.x;  
    va.x=(a.x+c.x)/2;  
    va.y=(a.y+c.y)/2;  
    vb.x=va.x-a.y+c.y;  
    vb.y=va.y+a.x-c.x;  
//    printf("%.3f %.3f %.3f %.3f\\n%.3f %.3f %.3f %.3f\\n",ua.x,ua.y,ub.x,ub.y,va.x,va.y,vb.x,vb.y);  
    double tmp=((vb.x-ua.x)\*(va.y-vb.y)-(vb.y-ua.y)\*(va.x-vb.x))/  
            ((ub.x-ua.x)\*(va.y-vb.y)-(ub.y-ua.y)\*(va.x-vb.x));  
//    printf("%.5f %.4f",tmp,ub.y-ua.y);  
    ans.x=ua.x+(ub.x-ua.x)\*tmp;  
    ans.y=ua.y+(ub.y-ua.y)\*tmp;  
    return ans;  
}  
point wr(point a,point b,double ang){  
    point ans=a;  
    ans.x+=(b.x-a.x)\*cos(ang)-(b.y-a.y)\*sin(ang);  
    ans.y+=(b.x-a.x)\*sin(ang)+(b.y-a.y)\*cos(ang);  
    return ans;  
}  
void solve(){  
    point c=cm(pt\[0\],pt\[1\],pt\[2\]);  
//    printf("%.2f %.2f\\n",c.x,c.y);  
    double mxx=-oo,mnx=oo,mxy=-oo,mny=oo;  
    double ang=2\*pi/n;  
    for(int i=0;i<n;i++){  
        point p=wr(c,pt\[0\],ang\*i);  
        mxx=max(mxx,p.x);  
        mxy=max(mxy,p.y);  
        mnx=min(mnx,p.x);  
        mny=min(mny,p.y);  
    }  
    printf("多角形 %d: %.3f\\n",++ff,(mxx-mnx)\*(mxy-mny));  
}  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    ff=0;  
    while(~scanf("%d",&n)&&n){  
        for(int i=0;i<3;i++){  
            scanf("%lf%lf",&pt\[i\].x,&pt\[i\].y);  
        }  
        solve();  
    }  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
}