The math for this is fairly simple. It'spounds per square inch.

Let's take your 800 lb. bike with tires inflated to 40 psi. The contact patch is 800lb./40 lb./sq. in. The 'lb.' terms cancel, leaving 800/40 sq. in., or 20 sq. in. This is exactly the 10 sq. in. you hypothesized. Lower pressure means more square inches, as does higher weight but, as you can see, it's very easy to calculate the area. It is not, however, 80 psi in any sense. It's 40 - in each tire.