i know the regular cross product gives the area of parallelogram, but how do i find the area of trapezoid?
You can partition any trapezoid into two triangles.
The area of any triangle is one-half the corresponding parallelogram:
$\displaystyle \frac{{\left\| {\overrightarrow a \times \overrightarrow b } \right\|}}
{2}$, where $\displaystyle \overrightarrow a \;\& \,\overrightarrow b $ are adjacent sides.