a trapezoid
/ TRAP-uh-zoyd /
Picture a tabletop seen edge-on that is wider at the bottom than the top, with the two slanted legs leaning in — a four-sided figure with exactly one pair of sides running parallel and the other pair not. That shape is a trapezoid. A road sign shaped like a wedge, a lampshade's silhouette, and the cross-section of a canal are everyday trapezoids.
Precisely, a trapezoid (called a trapezium in British English; the words are notoriously swapped between dialects, so always check) is a quadrilateral with at least one pair of parallel sides, called the bases. The non-parallel sides are the legs. The perpendicular distance between the two bases is the height. A trapezoid with its two legs equal in length is an isosceles trapezoid; that special case has equal base angles and a pair of equal diagonals, and it is the only kind of trapezoid that can be inscribed in a circle. The trapezoid median (or mid-segment) is the segment joining the midpoints of the two legs; it runs parallel to both bases and its length is the average of the bases, (b_1 + b_2)/2.
Trapezoids matter as the gateway to the parallelogram: weaken 'two pairs of parallel sides' to just one and you step from parallelogram up to trapezoid. The classic gotcha is the definition's wording. Under the 'exclusive' definition a trapezoid has exactly one pair of parallel sides (so a parallelogram is not a trapezoid); under the 'inclusive' definition it has at least one pair (so every parallelogram is a trapezoid). Both are in current use — and they give different answers to 'is a square a trapezoid?' — so a clean problem states which it means. The mid-segment result (b_1 + b_2)/2 holds either way.
A trapezoid has parallel bases of lengths 8 and 14. Its mid-segment, joining the midpoints of the legs, has length (8 + 14)/2 = 11 and runs parallel to both bases. If the legs are equal it is isosceles, its base angles are equal, and its diagonals come out equal.
The trapezoid median is the average of the two bases.
Beware the two conventions: 'trapezoid' (US) and 'trapezium' (UK) name the same one-pair-of-parallel-sides shape but the words are swapped between dialects, and 'exclusive' versus 'inclusive' definitions disagree on whether a parallelogram counts.