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Question

The medians BE and CF of a ABC intersect at G. Prove that area ( GBC)ar=AFGE.

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Solution

BE is the median of ΔABC
so, ar(ΔBEC)=12ar(ΔABC) __(1)
Median of triangle divides into 2 triangles of equal area.
Also CF is median of ΔABC
ar(ΔACF)=12ar(ΔABC) __(2)
from (1) and (2)
ar(ΔACF)=ar(ΔBEC)
ar(ΔGBC)+ar(ΔGEC)=ar(AFGE)+ar(GEC)
ar(ΔGBC)=ar(AFGE)


1339171_1269004_ans_fc0c2200e8374a43bee07b51a74ecd92.png

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