如图,已知 BC=3,D,E{BC} = 3,D,EBC=3,D,E 为 △ABC\bigtriangleup {ABC}△ABC 边 BC{BC}BC 上的两点，且满足 ∠BAD=∠CAE\angle {BAD} = \angle {CAE}∠BAD=∠CAE ， BD⋅BECD⋅CE=14\frac{{BD} \cdot {BE}}{{CD} \cdot {CE}} = \frac{1}{4}CD⋅CEBD⋅BE=41 ，则当 ∠ACB\angle {ACB}∠ACB 取最大值时， △ABC\vartriangle {ABC}△ABC 的面积等于___.
