How does the area of a trapezoid differ from that of a parallelogram?

The correct response highlights the distinct ways in which the areas of a trapezoid and a parallelogram are calculated, emphasizing their unique geometrical properties.

For a trapezoid, the area formula is specifically designed to accommodate its two parallel sides, known as the bases. The formula is given by 1/2 multiplied by the height and the sum of the lengths of the two bases, reflecting how the area is dependent on both the vertical height and the lengths of the bases. This recognizes that a trapezoid does not have opposite sides that are both parallel and equal, unlike a parallelogram.

In contrast, the area of a parallelogram is calculated simply as the base times the height. This formula reflects the property that in a parallelogram, the opposite sides are parallel and equal in length, and the height is the perpendicular distance between these two sides.

Thus, the correct choice effectively captures the differences in these area calculations: one involving the sum of two bases and halving that product while the other uses just one base multiplied by the height. This clarification enables a deeper understanding of the geometric properties that distinguish trapezoids from parallelograms.