By definition parallelograms are special type of trapezoids. Given a trapezoid with known sides one can calculate its area according to wikipedia. But in order to calculate the area of a parallelogram you need to know its height. I find this paradoxical. Can someone help clarifying this?
Edit: What I think I want to know is why trapezoid in general are solid(if that's the right word) but parallelograms are not. Rhombi are parallelograms. I can imagine changing a rhombus's diagonals (hence its area) without changing its sides.