Here is one way.

(1) Note that the trapezoid is isosceles.

(2) Find FG.

(3) Find FH and JG; thus, find HJ.

(4) Let A' and B' be projections of A and B, respectively, on DC. Since AD = BC, we have A'D = B'C. Find A'D and B'C.

(5) Find the height of the trapezoid AA' (and BB').

(6) Let E' be the projection of E to DC; then DE' = E'C = 5. The triangles DEE' and DBB' are similar. Find EE'.

(7) The area of EHJ is 1/2 (EE' - 1/2 AA') * HJ.