Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.
A
E D
T
B M C
Height of ABC = AM
Base of ABC = BC
[ ABC ] = (1/2) (BC) (AM) = 14 → (BC) (AM) = 28
Height of BEC = (1/2)AM
Base of BEC = BC
[ BEC ] = (1/2) (BC) (1/2)AM = (1/4)(BC) (AM) = (1/4) (28) = 7
+1341 
