a square
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This is the definition of a trapezoid. Two parallel sides, and two non-parallel. ■
There is no generic name. Any polygon with 4 or more sides can have 2 parallel sides. There are also non-polygonal shapes that can have parallel sides: for example, a circle that is stretched out into a cigar shape can have two parallel sides.
A trapezoid can be drawn to fit the description, as a trapezoid is a quadrilateral with two sides parallel and two sides nonparallel.
It depends on the actual shape of that octagon. It CAN have two pairs of parallel sides. A regular octagon has 4 pairs of parallel sides.
Quadrilaterals with two sets of parallel sides are parallelograms. Parallograms include squares, rectangles, and rhombi (rhombuses).