This is a trapezoid (or trapezum, depending on what country you live in).
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The only requirement for a trapezoid is that one pair of opposite sides be parallel. There could be trapezoids with a pair of perpendicular lines.
A right trapezoid has exactly one pair of perpendicular lines and is a quadrilateral.
a hexagon
The question contradicts itself. A dodecagon need not have any perpendicular sides.
If both pairs of opposite sides are parallel: A Rectangle, or a Square. If exactly one pair of opposite sides are parallel: An Isosceles Trapezoid. If it does not have parallel sides and one diagonal is the perpendicular bisector of the other: A Kite It is also possible that it does not have any parallel sides and neither diagonal is the perpendicular bisector of the other: A quadrilateral