Not a right cross-section.
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A cylinder has a circular cross-section whereas a cuboid has a quadrilateral cross-section.
Volume of a cuboid = cross-section area times its length
Yes. A cuboid, for example, has triangular cross sections
A square cross-section cuboid would fit the given description
Trapezoid. The rectangle, square, and rhombus are all parallelograms. The Trapezoid is a solid: a prism of trapezium cross-section.