Contact area

When two objects touch, only a certain portion of their surface areas will be in contact with each other.

Because objects are never perfectly flat due to asperities, the actual contact area (on a microscopic scale) is usually much less than the contact area apparent on a macroscopic scale.

Contact area may depend on the normal force between the two objects due to deformation.

The contact area between the two parallel cylinders is a narrow rectangle.

There isn't a simple derivation for sliding friction's independence from area.