It took me a while to figure it out, but we know that

BP = PD (deduced in the problem)

AB = CD = 4

because we were given a rectangle ABCD originally, and then we folded it.

S = (1/2) BP * CD = (1/2) PD * AB = 26/3

Now its easier to see PD is the base and AB is the height.

EDIT: your h in the diagram would have to correspond to the base BD