What would be an equivalent two-dimensional point
lattice for the area-centered hexagon?

Diagram is attached

The equivalent two-dimensional point lattice for the area-centered hexagon is a rhombus.

Explanation:

The area centered hexagon is illustrated with a centered figure that has dotted center and many other dots around it that connect each other.

In this case, we need to draw the area centered hexagon first.

After drawing, we then connect the centered atoms of the hexagon. This connected centered atoms now form a rhombus like shape

Note: The shape of a rhombus is said to be flat, and it has 4 equal sides.