This is a classic question concerning the intestinal tract, particularly the small intestine b/c that is where the most absorption in the digestive system takes place (that will be a question on your test...don't put stomach). The best way to think of this one is to remember that the more channels, the better. And, you can only have so many channels in a one area. So, more channels require more area (surface area). As far as the rate, think of a sand clock (the ones from board games). The reason they work is because you can only have so much sand fall down at each moment in time. This is why they can calibrate for an hour's time (rate). I.e., with more holes, it would empty quicker than one hour.
Be sure to keep in mind that the term "active" means that uses energy (ATP). In the sand example, the action is passive in that the sand isn't exerting energy; gravity is pulling the sand.
Additionally, passive transport (not requiring energy) is usually used before active for two simple reasons:
-why use energy when you don't have to?
-when there is enough ATP, typically too much ADP