The area of the event horizon of a black hole (A(eh)) is so far linked only with its entropy (S-BH). In this theoretical investigation, it is shown that relating A(eh) only to S-BH is inadequate, because Aeh is linked to the black hole's negentropy, which encompasses its entropy. Increasing A(eh) of black holes that grow now follows from the negentropy theorem (NET) and also from the well-known area theorem. The decreasing A(eh) of black holes that decay follows from the converse to NET and is not a violation of the area theorem. The corollary to NET is proved for the case when two dissipative structures merge, which is the basis for the coalescence of black holes. The converse of corollary to NET explains negentropy loss due to splitting of a dissipative structure. When applied to black hole explosion (i.e., splitting into an infinite number of parts), converse of corollary to NET reduces to converse of NET. The entropy/energy ratio of the exported Hawking radiance from black holes contributes to the entropy increase of the universe. These aspects justify the consideration of black holes as thermodynamic dissipative structures
