Question

Geometry:
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 810, then find the area of triangle AMN.

Answer 1

G divides each median in the ratio of 2 to 1 (the longer side goes from G to the angle)

triangle AMN is similar to triangle ABC (why?)
AMN is a scaled version of ABC (by a factor of ⅔)
its area should be scaled by (⅔)^2