In triangle △ABC, BE and CF are medians. BE=9, CF=12. If BE is perpendicular to CF, find the area of the triangle △ABC in cm2.
+128408 Call the intersections of the medians, D.....this is the centroid
And BD =(2/3) BE = (2/3)(9) = 6
And CF = (2/3)CF = (2/3) (12) = 8
So....triangle DBC is a 6-8-10 right triangle and its area = (1/2) (6)(8) =24
If we drew another median from A to BC....it would divide this triangle into 2 triangles with equal areas.....so the area of one of these triangles =12
And this triangle = 1/6 area of ABC
So [ ABC] = 6 * 12 = 72
