In the diagram, triangle ABC is isosceles with AB=AC, and AG is perpendicular to BC. Point D is the midpoint of AB, point F is the midpoint of AC, and E is the point of intersection of DF and AG. What fraction of the area of \triangle{ABC} does the shaded area represent?
Answer Choices
A. \frac{1}{12}
B. \frac16
C. \frac14
D. \frac{1}{10}
E. \frac18