In the diagram, G is the centroid of Triangle ABC If [ABC]=72 then what is [GME]
Barycentric coordinates!
G = (1,1,1)
M = (1/4, 1/4, 1/2)
E = (0, 1, 1)
det[G,M,E] = det[(1,1,1), (1/4,1/4,1/2), (0,1,1)] = 1/36
==> area of triangle GME = 72*1/36 = 2
The Median divides the triangle into two smaller triangles that have the same area.
[GME] = [ABC] / 24
+18 
