+772 Let ABC be a triangle. Let D be a point on side \overline{AC} such that line segment \overline{BD} bisects \angle ABC. If \angle A = 30^\circ, \angle C = 80^\circ, and AC = 12, then find the area of triangle ABD.
Give your answer in exact form, using radicals as necessary. You can write in \LaTeX, or for example write sqrt(2) to indicate \sqrt 2.
