The coefficient of friction (fr) is a number that is the ratio of the resistive force of friction (Fr) divided by the normal or perpendicular force (N) pushing the objects together.

I’m no scientist but it doesn’t sound like area of contact is really relevant to friction as a force. Where it may be more relevant is calculating how to overcome friction.

If you want to close your sliding glass door by smushing your hand to the glass pane and using the adhesion of your hand to slide the door, you’re using a lot of surface contact which can help slide the door. If you try the same thing with only one finger, you may not be able to do it. The amount of perpendicular force you need to push against the one part of glass the size of your fingerprint may crack the glass. Your hand spreads out the force over several square inches which.

But to calculate how much friction is happening between the door and the track it’s in, and how between your hand and the glass, separately will help determine how much force you need to slide that door closed.

This is all just a guess. I hope you find a more certain answer though!!