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Since we know the height (AD), we only need to find the base length (BC)
i: ABD = 60, but we don't know BAC or ACD, so we can only find the length of BD, not BC, which we need. ii: Again, we can find the length of DC, but not BC.
Combined: Since we can find BD from (i), and DC from (ii), we have BC and can find the area. Answer is C.
(1) Angle ABD = 60 --> triangle ABD is 30-60-90 triangle, so the sides are in ratio \(1:\sqrt{3}:2\) --> as AD=6 (larger leg opposite 60 degrees angle) then \(BD=\frac{6}{\sqrt{3}}\) (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient.
(2) AC=12, we can find DC. But we still don't know BD. Not sufficient.
(1)+(2) We know both BD and DC, hence we can find area. Sufficient.
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