The difference between the forces acting on the UPPER surface and the LOWER surface is the net force acting UPWARDS.
This net force is known as the BUOYANT FORCE.
Say, Force acting on the upper surface, F1 = P1 A
= h1pgA
Force Acting Underside, F2 = P2 A
= h2pgA
Net Force Acting Upwards = Buoyant Force
= Weight of Liquid Displaced = mg
Therefore, the buoyant force is equal to the weight of liquid displaced, which is in accordance with Archimedes' Principle