Friction is independent of the surface area!
It may sound counter-intuitive, since increasing the contact area would create a larger source of frictional forces. However, it also reduces the pressure between the two surfaces for a given force holding them together.
Since pressure equals force divided by the area of contact, it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting friction is then dependent only on the frictional coefficient of the materials and the FORCE holding them together.
For those interested, the frictional force is equal to the frictional coefficient multiplied by the normal force.
Some may ask, if friction is independent of surface area, why do F1 cars have wider tires? Rather than to increase friction, the wider tires serve to lower the pressures in the tires as well as even out the different frictional coefficients of the road.
Try explaining that the next time you watch an F1 race!