I5.4 Refer to the figure, $A B C D$ is a rectangle. $A E \perp B D$ and $B E=E O=\frac{c}{6}$. Find $d$, the area of the rectangle $A B C D$.
$\begin{array}{l}B O=4=O D=A O=O C \text { (diagonal of rectangle) } \\ A E^{2}=O A^{2}-O E^{2}=4^{2}-2^{2}=12 \text { (Pythagoras' Theorem) } \\ A E=2 \sqrt{3} \\ \triangle A B D \cong \triangle C D B \text { (R.H.S.) } \\ \begin{aligned} d & =2 \times \text { area of } \triangle A B D \\ & =\frac{2 \times(4+4) \cdot 2 \sqrt{3}}{2} \\ & =16 \sqrt{3}\end{aligned}\end{array}$