  In this paper we use the method of generalized gravitational entropy in
\cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical
entangling surface, and calculate the R\'enyi entropy with the dual bulk
gravity theory being either Einstein gravity or Lovelock gravity, this approach
is closely related to that in \cite{Casini:2011kv}. For a general entangling
surface we derive the area law of entanglement entropy. The area law is closely
related with the local property of the entangling surface.
