smc

Since $\angle C=90^{\circ }$, each of the three smaller angles is $30^{\circ }$, and $△BEC$ and $△CDF$ are both $30-60-90$ triangles. Defining the variables as illustrated above, we have $x=6\sqrt{3}$ from $△BEC$ Then $x-2=6\sqrt{3}-2$, and $y=\sqrt{3}(6\sqrt{3}-2)=18-2\sqrt{3}$. The area of the rectangle is thus $xy=6\sqrt{3}(18-2\sqrt{3})=108\sqrt{3}-36$. Using the approximation $\sqrt{3}\approx 1.7$, we get an area of just under $147.6$, which is closest to answer $\boxed{150}$. (The actual area is actually greater, since $\sqrt{3}>1.7$).