Employing the relationship between the black-hole thermodynamic functi
ons and the Euclidean path-integral approach to quantum gravity, we pr
ove, in the framework of four-dimensional Einstein gravity, that the e
ntropy of a stationary black-hole with a bifurcating Killing horizon s
urrounded by arbitrary classical matter fields is one quarter of the a
rea of the event horizon independent of the matter fields involved.