The medians AD, BE, and CF of triangle ABC intersect at the centroid G. The line through G that is parallel to BC intersects AB and AC at M and N, respectively. If the area of triangle ABC is 144, then find the area of triangle ENG.
So, I received this problem on Art of Problem Solving's Alcumus program, and I don't really have a clue as to how to solve it. I drew the picture, and I don't really see why there aren't multiple solutions. I struggle with any problems with words such as median, centroid, altitude, incenter, etc.
So, any ideas here?