I think conventionally you would expect the area of a polygon to be non-zero.
Generally your lecturer/teacher should specify in lectures the exact definition of things, and you should use that to answer his/her questions.
If you find loopholes you should ask them about it.
According to the link for Wikipedia you supplied:
In geometry a polygon is a flat shape consisting of straight lines
that are joined to form a closed chain or circuit.
Digging a little deeper you can find this at http://en.wikipedia.org/wiki/Closed_polygonal_chain:
In some cases it is important to draw a distinction between a
polygonal area and a polygonal chain.