Triangle FBC similar to triangle DBA
DB / DA = FB / FC
DB / 16 = FB / FC
Triangle FBC similar to triangle DHC
FB / FC = DH / DC
FB/FC = 5 / DC
DB / 16 = 5 / DC
80 = DB * DC
80 = DB * DB
80 = DB^2
DB = 4sqrt (5)
[ ABC ] = DB * DA = 4sqrt (5) * 16 = 64sqrt (5)
CORRECTED