I got 11sqrt3 but it wasn't correct

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half hexagon at the bottom = 3sqrt3

((3sqrt3/2)*2^2)/2

top triangle = 8sqrt3

edge length 2= long diagonal 4 << length from E to C

draw point halfway E to C to create point F

EF=CF=2

pythagorean theorem: DF= 2sqrt3

area of top triangle = DF*4 = 8sqrt3

add up= 10sqrt3