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There are several types of quadrilaterals that are not parallelograms or trapezoids (even assuming that you count rectangles, rhombi, and squares as parallelograms). Several types of these other parallelograms are:

- KITES: Kites are quadrilaterals that have two pairs of sides with equal lengths, but the sides with equal length are adjacent to each other as opposed to being parallel to each other. (For clarity, side A = side B and side C = side D, as opposed to a parallelogram where side A = side C and side B = side D.) Additionally, the angle between the non-equal sides is an obtuse or convex acute angle.
- DARTS: Darts are quadrilaterals that have two pairs of sides with equal lengths, but the sides with equal length are adjacent to each other as opposed to being parallel to each other. (For clarity, side A = side B and side C = side D, as opposed to a parallelogram where side A = side C and side B = side D.) Additionally, the angle between the non-equal sides is a concave acute angle. Fellow Expert Anand Mehta calls this type of shape an "arrowhead".
- There are other esoteric quadrilaterals like antiparallelograms, Watt quadrilaterals, and equilic quadrilaterals.
- However, the general catch-all term for any quadrilateral that is not a kite, dart, parallelogram, or trapezoid is an IRREGULAR QUADRILATERAL.

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A kite, an arrowhead, or simply a quadrilateral with no specific name.

Q: What is a quadrilateral that is not a parallelogram or a trapezoid?

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No, a trapezoid can't be a parallelogram. By definition, a trapezoid is a quadrilateral (four-sided figure) with only two parallel sides. A parallelogram, by definition, is a quadrilateral with two pairs of parallel sides.

quadrilateral

A quadrilateral is a parallelogram with four sides. For example: square, rectangle, parallelogram, trapezoid, rhombus, diamond...

Trapezoid, Parallelogram, Rhombus.

A parallelogram is a quadrilateral (four-sided polygon) containing TWO pairs of parallel sides. A trapezoid is a quadrilateral with ONE pair of parallel sides. Therefore a trapezoid is NOT a parallelogram. Note: Both terms are misspelled in the question. The correct spellings are TRAPEZOID and PARALLELOGRAM.

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a quadrilateral

a triangle

yes

triangle

A kite or a trapezoid

No.

No, a trapezoid can't be a parallelogram. By definition, a trapezoid is a quadrilateral (four-sided figure) with only two parallel sides. A parallelogram, by definition, is a quadrilateral with two pairs of parallel sides.

quadrilateral , trapezoid ,polygon ,not a parallelogram

no

No

a rhombus

Yes because a trapezoid and a parallelogram are both 4 sided quadrilaterals