What do we call a quadrilateral with both pairs of opposite sides parallel and equal in length?

A quadrilateral with both pairs of opposite sides parallel and equal in length is defined as a parallelogram. This definition encompasses several specific types of parallelograms, including rectangles and rhombuses, but the general term that applies to any quadrilateral meeting these criteria is parallelogram.

In a parallelogram, opposite sides are not only parallel but also equal, which allows for specific properties such as congruent opposite angles and the ability to find the area by multiplying the base by the height. This makes it a fundamental shape in geometry. The other options, while they include shapes that have some similar properties, do not correctly describe a quadrilateral that fulfills the condition of having both pairs of opposite sides parallel and equal. For instance, a rectangle has right angles but does not specifically emphasize the sides' equality beyond the necessary opposite sides being equal, while a rhombus emphasizes equal side lengths without the requirement of having right angles. A trapezoid, on the other hand, has only one pair of opposite sides that are parallel, which does not satisfy the criteria given in the question. Thus, the correct answer identifies the broadest definition fitting the described properties of the shape.