Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle AMC if [ABC]=180.

Extract the useful information: M is the midpoint of BC.

Then triangle AMC has half the base of triangle ABC, and the same height.

The area of triangle AMC would be half that of triangle ABC, so the answer is 90.