Note that trapezoids ACFD and BCFE are similar, so the sides are in proportion to each other.
(80 + 120)/120 = 210/z
Solve for z. I get z = 126. Thus y + z = 210 gives y = 84.
(80 + 120)/120 = 90/x
I get x = 54.
A = (1/2)(b1 + b2)h
where b1 and b2 are the parallel "bases" and h is the perpendicular distance between the bases (the "height"). As these are "right" trapezoids getting the height is easy. And you now have the measurements for each side.
I get the area of trapezoid BCFE is 5040 and the area of trapezoid ACED is 5760.