Even if you did not complete the section of surface area, do note that surface is not in the friction equation. Can you explain why not?
Large area of contact is the reason of the frictional force between the surfaces and it also causes the resuction in the pressure holding the two surfaces for the fiven force holding them together.
Pressure equals the force divided by the area of contact. So increase in the friction generating area reduces the pressure. So the frictional forces then depend only on the frictional coefficient of the materials and the Force holding them together.
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