Aplane intersects a prism parallel to the base of the prism. the cross section is a polygon with eight sides. how many sides does the base of the prism have?

The plane of cross section and the basis plane are parallel, so each lateral face of the prism is intersected by parallel planes and their intersection lines are parallel.

Since the cross section is a polygon with eight sides (each side of this polygon is parallel to coresponding side of basis), then basis is also a polygon with eight sides.