trapezoid and paralellogram are both quadrilaterals
the heiarchy is
quadrilaterals are 4 sided figures
quadrilaterals is split up into
 A. no pairs of paralell sides
 - kite
 B. 1 pair of paralell sides
 - trapezoid/trapezium
 C. 2 pairs of parell sides (paralellograms)
 -rectangles
 -rhombus
 -square
so you can see that they are both quadrilaterals (quad=4, lateral=sides, quadrilateral=4 sided figure)