question ___1

Question

Answer 1

Solution: 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*√3)

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)

(θ=30)

therefore, the total area =2(area(ABD))

=32/(3√3) sq. unit