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