is parallelogram a type of trapezoid?

Hi, I do not know what official OG defines this but in my opinion, a parallelogram qualifies the definition of a trapezoid.
Trapezoid: one pair of opp sides are parallel
Parallelogram: both the pairs of opp sides are parellel

e.g. For the following parallelogram ABCD,

Area of a trapezoid is given by [(a+b)/2]*h

For a parallelogram, a=b; thus, area of trapezoid becomes (2a/2)*h = ah

The definition of area of a parallelogram is = ah

In both the cases we get the same result, thus, mathematically a parallelogram qualifies the definition of a trapezoid.

I love this question. Haha--this should never matter in our lives and yet it does! The answer in short is no one knows but there is a preference for YES!

From the Trapezoid Wiki:

Definition

There is also some disagreement on the allowed number of parallel sides in a trapezoid. At issue is whether parallelograms, which have two pairs of parallel sides, should be counted as trapezoids. Some authors[2] define a trapezoid as a quadrilateral having exactly one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. Other authors[3] define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition[4]), making the parallelogram a special type of trapezoid. The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make such concepts as the trapezoidal approximation to a definite integral ill-defined. This article uses the inclusive definition and considers parallelograms as special cases of a trapezoid. This is also advocated in the taxonomy of quadrilaterals.

Parallel sides does not make it a parallelogram. 2 pairs of parallel side do.