UKMT Junior Kangaroo, 2016

The diagram shows a rectangle $ABCD$ in which $AB = 1$ metre and $AD = 4$ metres. The points $E$ and $G$ are the midpoints of $AD$ and $AB$ and the points $F$ and $H$ are the midpoints of $AE$ and $AG$. What is the area of the shaded rectangle?

(A) $\frac{1}{16}$ m$^2$ (B) $\frac{1}{8}$ m$^2$ (C) $\frac{1}{4}$ m$^2$ (D) $\frac{1}{2}$ m$^2$ (E) $1$ m$^2$