Strictly speaking you cannot have one parallel side - you must have one pair.
Any irregular polygon with four or more sides can have a pair of parallel sides. Most have no specific names - the only one that does is a trapezium.
A quadrilateral in the shape of a kite has no parallel sides
Any shape wit four of more sides can have one pair of parallel sides.
A trapezoid has exactly one pair of parallel sides
trapezoid
A trapezoid has only one pair of parallel sides
Trapezoid
A geometric shape with only one set of parallel sides is a trapezoid.
A quadrilateral in the shape of a kite has no parallel sides
A trapezium. It has one set of parallel sides. It has four sides.
Any shape wit four of more sides can have one pair of parallel sides.
A trapezoid has exactly one pair of parallel sides
trapezoid
trapezium
I think this person means the trapazoid. It has only one pair of parallel sides.
A trapezoid has only one pair of parallel sides
A trapezoid has only one pair of parallel sides of different lengths.
The name of the four-sided shape that has only one pair of parallel sides is known as a trapezoid. The other two sides are not parallel to each other. There are many other shapes with more than four sides that have one pair of parallel sides but these typically don't have special names. So assuming the question is only referring to four-sided figures, the answer is a trapezoid.