C :

#include <math.h>

linepoints(double x1, double y1, double x2, double y2,
           double *a, double *b, double *c) {
   *a = y2 - y1;
   *b = x1 - x2;
   *c = *a * x1 + *b * y1;
}

bi(double x1, double y1, double x2, double y2, double *a, double *b, double *c){
   *a = 2*(x2-x1);
   *b = 2*(y2-y1);
   *c = x2*x2 + y2*y2 - x1*x1 - y1*y1;
}

isct(double a, double b, double c, double aa, double bb, double cc,
     double *x, double *y){
   double det = a*bb - b*aa;
   if (fabs(det) < 1e-10) return 0;
   *x = (-b*cc + c*bb)/det;
   *y = (a*cc - c*aa)/det;
   return 1;
}

int nd, done[200];
int i,j,k;

struct pp {
   double a, b, c;
} p[100];

double x,y,xx,yy,a,b,c;

int np, i,j,j;

char hc[20];

double xa, xb, ya, yb, area, triarea;
int nx;

main(){
   linepoints(0,0,0,10,&a,&b,&c);
   p[np].a = a; p[np].b = b; p[np++].c = c;
   linepoints(0,10,10,10,&a,&b,&c);
   p[np].a = a; p[np].b = b; p[np++].c = c;
   linepoints(10,10,10,0,&a,&b,&c);
   p[np].a = a; p[np].b = b; p[np++].c = c;
   linepoints(10,0,0,0,&a,&b,&c);
   p[np].a = a; p[np].b = b; p[np++].c = c;

   while (3 == scanf("%lf%lf %s",&xx,&yy,hc)) {
      if (strcmp(hc,"Colder")) bi(x,y,xx,yy,&p[np].a,&p[np].b,&p[np].c),np++;
      if (strcmp(hc,"Hotter")) bi(xx,yy,x,y,&p[np].a,&p[np].b,&p[np].c),np++;
      area = 0;
      nd = 0;
      for (i=0;i<np;i++) {
         nx = 0;
         for (j=0;j<np;j++) {
            if (isct(p[i].a,p[i].b,p[i].c,p[j].a,p[j].b,p[j].c,&x,&y)){
               int isin = 1;
               for (k=0;k<np;k++) {
                  if (p[k].a*x + p[k].b*y - p[k].c < -.000001) isin = 0;
               }
               if (isin) {
                  if (!nx) {
                    nx++;
                    xa = x;
                    ya = y;
                  } else if (nx<2 && (fabs(x-xa)>.000001 || fabs(y-ya)>.000001)) {
                    nx++;
                    xb = x;
                    yb = y;
                  }
               }
            }
         }
         if (nx == 2) {
            for (j=0;j<nd;j++) {
               if (fabs(p[i].a*p[done[j]].b - p[i].b*p[done[j]].a) < .000001
                 && fabs(p[i].a*p[done[j]].c - p[i].c*p[done[j]].a) < .000001
                 && fabs(p[i].b*p[done[j]].c - p[i].c*p[done[j]].b) < .000001)
                 break;
            }
            if (j == nd) {
               done[nd++] = i;
               triarea = -p[i].c / hypot(p[i].a,p[i].b) * hypot(xa-xb,ya-yb) / 2;
               area += triarea;
            }
         }
      }
      if (nd < 3 || area < .000001) area = 0;
      printf("%0.2lf\n",area);
      x = xx; y = yy;
   }
}