It may seem strange but friction is independent of the actual area of contact. The reason behind this is that the actual area of contact on an atomic scale is a fraction of the total surface area.
Friction happens due to the interatomic forces at these minute regions of atomic contact. The fraction of the geometric area in atomic contact is proportional to the normal force divided by the geometric area. If the normal force is doubled, the area of atomic contact is also doubled and the friction becomes twice as large. But, if the geometric area is doubled whilst the normal force remains the same, the fraction of area in atomic contact is halved and the actual area in atomic contact hence the friction force remains constant.