Is contact patch area governed by A=W/P contact_patch_area = weight / tire_pressure


Is this true? 


Wikipedia says "mostly". 
This guy analyzed some automobile tire manufacturer, and although the info was self-conflicting, he concludes that it very much depends on tire construction, but the equation is for sure false. However, he bases some of the conclusions on the assumption that rubber acts as a constant-rate spring, which it doesn't.
This answer assumes it is true.
Assuming a 200 pound rider+bike+clothes+load and a tyre pressure of 100 PSI, and a nice even 50/50 weight distribution, then each wheel is supporting 100 pounds and should have a contact patch size of 1 square inch.

You could empirically measure this using a scale and a dry piece of paper, and a slightly dampened tyre.   Moisten the tyre and use its "footprint" on the paper.  Do the same with the rear wheel.  And then draw around the boundary with a pen.
Perhaps a dusting of talc powder on the tyre would work better than water.