SOLUTION: Equilateral triangle ABC has altitude AD of length 12 mm. Median AE of triangle ABD is drawn. What is the area of triangle AEC in mm²?

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Question 1172767: Equilateral triangle ABC has altitude AD of length 12 mm. Median AE of triangle ABD is drawn. What is the area of triangle AEC in mm²?
Answer by greenestamps(13200) About Me  (Show Source):
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Triangles ABD and ACD are 30-60-90 right triangles, with long leg AD having length 12. The side length of triangle ABC is then 12%2A%282%2Fsqrt%283%29%29+=+24%2Fsqrt%283%29+=+8%2Asqrt%283%29.

AD is half that side length, or 4%2Asqrt%283%29; ED is half again as much, or 2%2Asqrt%283%29.

So the base of triangle AEC has length 6%2Asqrt%283%29.

Then the area is one-half base time height:

%281%2F2%29%286%2Asqrt%283%29%29%2812%29+=+36%2Asqrt%283%29