The only classification I could give this figure would be that it is a trapezoid, perhaps.
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A quadrilateral
The name for a quadrilateral with 4 sides of all different lengths is simply "quadrilateral". All of the specializations of quadrilaterals: parallelogram, trapezoid, kite, rhombus, rectangle, and square, have at least one pair sides with the same length.
A regular polygon has all sides equal in lengths. A quadrilateral is a 4 sided polygon.
this isn't possible, as having all sides be different lengths would prevent the sides from being parallel.
A trapezoid in the UK is a trapezium which is a 4 sided quadrilateral with 1 pair of opposite parallel sides of different lengths.