Medians Triangle Area

In △ABC, medians AD & BE intersect at G and ED is drawn. If the area of △EGD = k, find the area of △ABC.

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Look at △BED. Medians intersect in the ratio 2:1, so set BG = 2x and GE = x.

Thus the area of △BGD is two times the area △GED = 2k.

Then look at △BEC. Area △BED = △CED. △BED = 3k so △CED = 3k too.

Now consider △ADC.
△AED = △CED, so △AEG = 2k.

Finally, look at △BAC.
△BAE = △BCE = 6k, so △BAG = 4k.

So we’ve got 12k total.

(There might be snazzier ways to get to it.)

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