Answer:
C
Step-by-step explanation:
Remark
The large triangle with 2 60 degree angles is equilateral. Therefore the line at D can be shown to be at right angles to AB and D is the midpoint of AB.
Solution
1/2 of AB is 6 See the discussion above.
DB is the base of CBD in the right triangle CDB
h^2 + DB^2 = 12^2
h^2 + 6^2 = 12^2
h^2 = 144 - 36
h^2 = 108
h = sqrt(108)
h = sqrt(9*3 * 4
sqrt(9) = 3
sqrt(4) = 2
So the square root of 108 = 3*2 sqrt(3) because there is 1 three that is left over.
h = 6*sqrt(3)
base = 12
Area = 1/2 * 6*sqrt3) * 12
Area = 36 sqrt(3)
The answer is C
