  The fixed area states are constructed by gravitational path integrals in
previous studies.In this paper we show the dual of the fixed area states in
conformal field theories (CFTs).These CFT states are constructed by using
spectrum decomposition of reduced density matrix $\rho_A$ for a subsystem $A$.
For 2 dimensional CFTs we directly construct the bulk metric, which is
consistent with the expected geometry of the fixed area states. For arbitrary
pure geometric state $|\psi\rangle$ in any dimension we also find the
consistency by using the gravity dual of R\'enyi entropy. We also give the
relation of parameters for the bulk and boundary state. The pure geometric
state $|\psi\rangle$ can be expanded as superposition of the fixed area states.
Motivated by this, we propose an area operator $\hat A^\psi$. The fixed area
state is the eigenstate of $\hat A^\psi$, the associated eigenvalue is related
to R\'enyi entropy of subsystem $A$ in this state. The Ryu-Takayanagi formula
can be expressed as the expectation value $\langle \psi| {\hat
A}^\psi|\psi\rangle$ divided by $4G$, where $G$ is the Newton constant. We also
show the fluctuation of the area operator in the geometric state $|\psi\rangle$
is suppressed in the semiclassical limit $G\to0$.
