consider the point of intersection of AD and BE as O.
now as BAD=30 and ABE is 60
therefore AOB=90.
also we know that median divides a triangle into two equal areas.
area of ABD=area of ADC
also O is centroid.
therefore AO=(2*4/3)=8/3
sin(60)=AO/AB
AB=16/(3*root(3))
now you know AD,AB and angle between the two i.e. 30
so area(ABD) =1/2*AB*AD*sin(theta)= 16/(3*root(3))
(theta=30)
therefore, the total area =2(area(ABD))
=32/(3*root(3))
