Answer:
(C) 1/2
Explanation:
Recognize that each of the side lengths of the triangle joining midpoints is half the corresponding side length of the outside triangle. Since its scale factor is 1/2, the area of the "midtriangle" is 1/4 that of the outside triangle.
In this figure, triangle DEF is the fourth "midtriangle" of ABC, its area is ...
... (1/4)^4 · 128 = 128/256 = 1/2