Why some photodetectors have large areas?
A larger area means it can collect more light power and hence it becomes more sensitive. The down side is that capacitance is increased and the response time falls off making a large area photodiode quite unsuitable for high speed comms applications.

It's a the same reasoning behind a satellite dish - a bigger dish collects more power from a remote transmission and produces a bigger signal. Hence why voyager 1 and 2 had quite large dishes for comms with earth.