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?

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) (Show Source): You can put this solution on YOUR website!

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 .

AD is half that side length, or ; ED is half again as much, or .

So the base of triangle AEC has length .

Then the area is one-half base time height:

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