Problem: In triangle ABC,D is the midpoint of AB;E is the midpoint of DB; and F is the midpoint of BC. If the area of â–³ABC is 96, then the area of â–³AEF is
Answer Choices:
A. 16
B. 24
C. 32
D. 36
E. 48
Solution:
Since F is the midpoint of BC, the altitude of â–³AEF from F to AE (extended if necessary) is one half the altitude of â–³ABC from C to AB (extended if necessary ). Base AE : of â–³AEF is 3/4 of base AB of â–³ABC. Therefore, the area of â–³AEF is (1/2)(3/4)(96)=36.