## Online Course Discussion Forum

### Winter Camp 2018 Blue Geometry question 3

Let G be the centroid of triangle ABC, AG is 3, BG is 4, CG is 5, find the area of ABC

Extend line $AG$ to a point $H$, so that $GH = 3$. Then $GBHC$ is a parallelogram with sides $4$ and $5$, and one of its diagonals of length $3$ (why?). What else can you say about this parallelogram? Can you find its area? How does the area of this parallelogram relate to the area of the triangle?

* Recall that the centroid splits each median in a $2:1$ ratio, and the $6$ triangles made up by the medians all have the same area.

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