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The thermodynamics of the Kerr-AdS black hole is re-formulated within the context of the formalism of geometrothermo-dynamics (GTD) and the cosmological constant is considered as a thermodynamical parameter. We conclude that the mass of the black hole corresponds to the total enthalpy of this system. Choosing appropriately the metric in the manifold of equilibrium states, we study the phase transitions as a divergence of the thermodynamical curvature scalar. This approach reproduces thefatcat:ixscmpkj5zehpl2iyeq7cfzfaq