As with the triangle, the trapezoid presents a challenge due to the partial square units that are cut by the sides. However, if we duplicate the trapezoid and arrange the pieces so a corresponding pair of legs are aligned and the bases are on opposite sides as the original, the resulting shape is a parallelogram. We know the shape formed by the two trapezoids together is a parallelogram because: 

• the corresponding legs of the trapezoids have the same length and slope so they fit together exactly and form a quadrilateral,

• the corresponding legs that aren't aligned have the same slope and are parallel

• the bases of the trapezoids were already parallel and since they have the same height, the combined bases also form straight, parallel sides.

Note: The justification above for why the combined trapezoids form a parallelogram is provided for completeness. At the middle school level, this deductive proof is probably not expected from the students. However, students should be able to be convinced that because the longest sides and slopes of the triangles are equal there should be no overlap of the pieces. This allows students to explain why the area of the original trapezoid is half the parallelogram. Further, students should be able to visually identify that the pairs of opposide sides appear to be parallel.

Note: Interestingly, the terms trapezoid (a quadrilateral with at one pair of parallel sides) and trapezium (a quadrilateral with no parallel sides) in American English have the reverse definitions in British English so it is important to be aware of this difference if you have international students in your classroom. 

It can also be helpful to attend to whether your curriculum materials define a trapezoid as having exactly one pair of parallel sides or at least one pair of parallel sides so that if students are classifying shapes they know whether or not a square, rectangle, or parallelogram should also be considered a trapezoid. It can also be helpful for students to know that the definition is not universally consistent if they encounter an alternative definition in the future.