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Answer:
C. 36√3 square units
Step-by-step explanation:
Your knowledge of special triangles tells you that height CD is ...
CD = 6√3
so the area is ...
A = 1/2bh
A = 1/2(12)(6√3) = 36√3 . . . . square units
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<em>Additional comment</em>
The 30°-60°-90° right triangle that is half an equilateral triangle has a short side equal to half the length of the long side. The Pythagorean theorem tells you that the middle-length side is √(2²-1²) = √3 times the shortest side. That is, the side length ratios in this "special" triangle are ...
1 : √3 : 2
This means the length DB is 12/2 = 6, and the length CD is 6√3.
