In rectangle A B C D, A B=1, B C=2, and points E, F, and G are midpoints of \overline{B C}, \overline{C D}, and \overline{A D}, respectively. Point H is the midpoint of \overline{G E}. What is the area of the shaded region?
Answer Choices
A. \dfrac{1}{12}
B. \dfrac{\sqrt{3}}{18}
C. \dfrac{\sqrt{2}}{12}
D. \dfrac{\sqrt{3}}{12}
E. \dfrac{1}{6}