G8.1 If the area of the rectangle $A B C D$ is $a+4 \sqrt{3}$, find the value of $a$.
The lines joining the centres form an equilateral triangle, side $=2$.
$$
\begin{array}{l}
A B=2+2 \sin 60^{\circ}=2+\sqrt{3} \\
B C=4
\end{array}
$$

Area of $A B C D=(2+\sqrt{3}) \times 4=8+4 \sqrt{3}$
$$
a=8
$$