Which solid figure has parallel polygonal ends that are equal in size and shape, and whose sides are parallelograms?

The solid figure described is a prism. A prism is defined by having two parallel polygonal ends, known as bases, that are congruent, meaning they are equal in size and shape. The sides of the prism are parallelograms, which connect the corresponding sides of the two bases.

This specific characteristic of having parallel, congruent polygonal bases sets prisms apart from other three-dimensional shapes. For example, pyramids have a single polygonal base with triangular faces that converge to a point, making their sides not parallelograms. Meanwhile, a cube is a special type of prism where the bases are squares, but the term "prism" captures a broader range of shapes that include any polygonal bases, not limited to squares. Lastly, a cylinder has circular bases and not polygonal ones, which does not fulfill the requirement of the bases being polygons. Thus, the correct identification of the figure with parallel polygonal ends connected by parallelogram sides is indeed a prism.