3420.29 – Midline Triangle
In a random triangle ABC, D is the midpoint of AB; E is the midpoint of BD; and F is the midpoint of BC.
Suppose the area of ABC is . Then the area of AEF is:
Solution
The figure described in the problem is drawn below. Note that if you halve the base of a triangle and don't change the altitude, you halve the area. Therefore,
