You have asked a good question that doesn't really have a straight answer. There are actually two accepted definitions of what a trapezoid is. If you use the definition known as the exclusive definition, then parallelograms and squares are not trapezoids. This is because the exclusive definition says that a trapezoid has exactly two parallel sides; since squares and parallelograms have two pairs of parallel sides, they do not qualify as trapezoids under this definition.
The inclusive definition says that a parallelogram has at least two parallel sides; in this case, squares and parallelograms are included in the group.
If you need to answer this question for a class, I would suggest you ask your instructor which definition he or she wants students to use.