I have a question about the coefficient of kinetic friction

I have a question about the coefficient of kinetic friction?
If you pulled the block along its small edge, both the coefficient of kinetic friction and the force of friction would be the same as for the block on its large surface. Explain why they should be the same. Hint: think of surface contact and mass.

The friction force depends only on the weight of the block, which in turn depends only on its mass.

If there is a smaller surface area, the mass exerts a correspondingly greater pressure (force per unit area) which keeps the coefficient of kinetic friction (k) the same also.

Conversely a greater surface area means a lower pressure between the surfaces.

So the friction force f = k*m*g is always the same.