Solution: consider the point of intersection of AD and BE as O.
now as BAD=30 and ABE is 60
also we know that median divides a triangle into two equal areas.
area of ABD=area of ADC
also O is centroid.
Now you know AD,AB and angle between the two i.e. 30
so area(ABD) =1/2*AB*AD*sin θ= 16/(3*√3)
therefore, the total area =2(area(ABD))
=32/(3√3) sq. unit