The centroid of triangle ABC is G. Given AD = 15 and BE = \(25\), find the area of triangle ABC.
+128407 By a property of the medians
EG = 25 (1/3) = 25 / 3
AG = 15 (2/3) = 10
Since triangle AGE is right...its area = (1/2)product of legs EG and AG = (1/2)(25/3)(10) = 250 / 6
And by another median property, this area = 1/6 the area of ABC
So
[ ABC ] = 6 (250 / 6) = 250 units ^2
