The pressure exerted by a liquid at the base of a container is given by the formula $P = P_{atm} + \rho g h$, where $\rho$ is the density of the liquid, $g$ is the acceleration due to gravity, and $h$ is the height of the liquid column .

1. Dependency: The formula shows that pressure depends only on the vertical height ($h$) and the density of the fluid ($\rho$). It is independent of the shape of the vessel or the total volume/mass of the liquid contained .
2. Application: Since both vessels A and B are filled with the same liquid (water) to the same vertical height ($h$), the pressure at the base of both vessels is identical.
3. Hydrostatic Paradox: This counter-intuitive result, where pressure is independent of the volume or shape, is known as the hydrostatic paradox .

Note: While the pressures are equal, the thrust (Force = Pressure $\times$ Area) on the base would also be the same because the base areas are equal. However, the total weight of the liquid would differ because the volumes differ.