How is friction force related to the surface area?

Hint : Friction force is defined as the force which resists the relative motion of the solid surfaces, fluid layers, and the material elements sliding against each other. It is the external force that opposes the relative motion between the two surfaces in contact.

Complete Step by step answer:
The force due to the friction is independent of the contact area in between the two surfaces. But this relationship breaks down if the surface area becomes too small and due to this the coefficient of friction increases as the object may dig into the surface.
In general, the friction is independent of the actual area of the contact and this is due to the reason that the actual area of the contact on an atomic scale is a fraction of the total surface area. It is due to the interactive forces of the atomic contact.
Also, the friction depends on the condition of the surface in contact with. A surface having a smooth surface area will have less frictional force between the two surfaces and similarly, if the object has a rough surface area then it will have a higher frictional force.

Note:
1. Shear force and Viscous force are the forces that depend on the surface area.
2. The force of friction does not depend on the area of the contact. Friction slows a moving object down.
3. Friction force depends on the nature of the surfaces in contact and the materials that are in contact. It depends on the smoothness or roughness of the two surfaces that are in contact.