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 DMT is [ABC] = \(160\).
Note that since AM is a median of triangle ABC, then BM = MC
And triangles ABM and ACM are equal because they are on equal bases with equal heighs
Looking at triangle ABM, ME and BD are medians and we can construct median AF in this triangle
These medians create 6 equal areas in the triangle
[ ABM ] = [ACM ] = (1/2)[ABC ] = 80
[ DMT ] = [ ABM ] / 6 = 80 / 6 = 40 / 3