In square A B C D, points E and H lie on \overline{A B} and \overline{D A}, respectively, so that A E=A H. Points F and G lie on \overline{B C} and \overline{C D}, respectively, and points I and J lie on \overline{E H} so that \overline{F I} \perp \overline{E H} and \overline{G J} \perp \overline{E H}. See the figure below. Triangle A E H, quadrilateral B F I E, quadrilateral D H J G, and pentagon F C G J I each has area 1 . What is F I^{2} ?

**Answer Choices**

A. \dfrac{7}{3}

B. 8-4 \sqrt{2}

C. 1+\sqrt{2}

D. \dfrac{7}{4} \sqrt{2}

E. 2 \sqrt{2}