Find the area of the shaded portion. show all work for full credit.

Draw some lines and we get some special 30-60-90 triangless
se diagram

so using my math
remember that if the hyptonuse is 2x then angle oposite the 30 degree is x and angle oposit the 60 degree is x√3

so

we have a kite and know the lengths of he diagonals
we do

(9+3) times (3√3) to find the area total which is 36√3

then, we find teh area of the sector not shaded
the area of the sector is (120/360) times the area which is pi6^2
so
1/3 times 36pi or 12pi
so

36√3-12pi≈24.6547 square units