(Note the maximizing of surface area to the direction of travel.)
I'm gonna be nitpicky and ask if what you actually mean is perpendicular to direction of travel, not just the direction of travel. I mean imagine a pyramid falling upside down at terminal velocity. Well, there's actually a rather large amount of surface area in the direction of travel, more so than if it were falling the right way up with a flat square breaking the fall. Yet upside down it will fall faster, not slower.