A quadrilateral. (There isn't a more specific word for it.)
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A trapezium is a quadrilateral with two parallel lines.
It is called a Rhombus.
TRAPEZOID
I don't think this is possible. there is not a quadrilateral with these qualities. If it is a quadrilateral, it will automatically have parallel lines, but there is not one that has both. The closest one would be the trapezoid, with a set of parallel lines, but no right angle. The square and rectangle have two sets of parallel lines and 4 right angles.
It is not possible to have a quadrilateral with four parallel sides - this would bea series of four parallel lines that do not intersect.A quadrilateral with four sides of equal length is a rhombus, however.And a quadrilateral with 2 pairs of parallel sides is a parallelogram.