Answer:
may or may not be
Step-by-step explanation:
Because we only know two sides, A-center and C-center, we cannot verify that ABCD is a parallelogram. Corner D could be 40 units away from the center, and Corner B might be 12 units away. If you imagine pulling back the corners (away from the center), the length between two corners can be equal even if the shape is not parallel.
For example, BC could have a length of 10, and AD could have a length of 15. These sides could be at completely different angles/slants (so they might not be parallel), and still maintain a middle measurement of 4.0 on both sides.
However, all sides could be parallel, but we are not provided enough information to confirm this possibility.