  Based on the perturbation expansion, we compute the noncommutative
corrections to the minimal surface areas of the pure AdS spacetime and
Schwarzschild-AdS black hole, where the noncommutative background is suitably
constructed in terms of the Poincar\'e coordinate system. In particular, we
find a reasonable tetrad with subtlety, which not only matches the metrics of
the pure AdS spacetime and Schwarzschild-AdS black hole in the commutative
case, but also makes the corrections real rather than complex in the
noncommutative case. For the pure AdS spacetime, the nocommutative effect is
only a logarithmic term, while for the Schwarzschild-AdS black hole, it
contains a logarithmic contribution plus both a mass term and a noncommutative
parameter related term. Furthermore, we show that the holographic entanglement
entropy with noncommutativity obeys a relation which is similar to the first
law of thermodynamics in the pure AdS spacetime.

High Energy Physics - Theory;General Relativity and Quantum Cosmology