  We resolve the controversial issue of the geometric approach to the black
hole thermodynamics. The geometric description of the equilibrium
thermodynamics comes from Ruppeiner geometry based on a metric on the
thermodynamic state space. For this purpose, we consider the
Reissner-Nordstr\"om-AdS (RN-AdS) black hole which provides two different
ensembles: canonical ensemble for fixed-charge case and grand canonical
ensemble for fixed-potential case. Two cases are independent and cannot be
mixed into each other. Hence, we calculate different Ruppeiner curvatures for
two ensembles. However, we could not find the consistent behaviors of Ruppeiner
curvature corresponding to those of heat capacity. Alternatively, instead of
the Ruppeiner curvature, we newly propose the curvature scalar in the 2D
dilaton gravity approach which shows the features of extremal, Davies and
minimum temperature points of RN-AdS black hole, clearly.
