No, unless you call a rectangle a trapezoid.
Recall the formula for the area of a parallelogram: [tex]bh[/tex]. Recall the area for a trapezoid: [tex]\frac{b+b_1}2h[/tex] (a trapezoid has two bases).
Suppose they did have the same area. Then [tex]bh=\frac{b+b_1}2h[/tex] and [tex]2b=\frac{b+b_1}[/tex] and [tex]b=b_1[/tex].
So the only way for their areas to be equal is for the trapezoid to have the same base on top and bottom. That means the trapezoid must be a rectangle. Most people don't say a rectangle is a trapezoid, so no.
