If somebody can explain the sample test case, in my opinion average should be (0.5 +0.5+0.5)/3 which is 0.5

it is easy

double a = 0;
Random r = new Random();
int nit = 1000000;
for(int it=0;it<nit;++it){
    double ax = 0, ay = 0;
    double bx = r.nextDouble(), by = r.nextDouble();
    double cx = r.nextDouble(), cy = r.nextDouble();
    a+=Math.abs(bx*cy-cx*by)/2;
}
out.println(a/nit);