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In the diagram, G is the centroid of Triangle ABC If  [ABC]=72 then what is  [GME]

 Nov 15, 2020
 #1
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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

 Nov 15, 2020
 #2
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The Median divides the triangle into two smaller triangles that have the same area.

 

[GME] = [ABC] / 24 laugh

 Nov 15, 2020

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