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Yes. Quadrilaterals means a closed shape with four sides, and a trapezoid has four sides, and is a closed shape.
hexagons, triangles, rectangles, trapizoids, and many other shapes. circles do not tessallate
No. Parallelograms are never trapezoids because in order to be a parallelogram there has to be two sets of parallel sides. A trapezoid only has one set of parallel sides.
Four sided figures are called quadrilaterals. They are usually squares, rectangles, trapizoids, etc..