1. The problem statement, all variables and given/known data The following is a geometry question I can't seem to get. "Consider an acute angle △ABC. Points D, E, F are mid points of sides BC, CA and AB respectively. G is the centroid of △ABC. Area of △AFG = 14, EC = 15/2. Perpendicular distance of F from BC = 6. Find BC2−AB2 " 2. Relevant equations - 3. The attempt at a solution Here is the figure that I have drawn - From EC =15/2 I get AE=15/2 So AC =15 . But what now? How can I utilize the fact that FK=6 and Area(AFG)=14 in finding BC2−AB2 ? Is Area of AFG = Area of FGB = Area of GBD ... ? If so then area of ABC 14*6=84 . Is that right ? Then altitude from A = 6*2=12 Thus BC = 84/6 = 14 . But how to figure out AB ?