8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6d1485a6-e52b-4492-8d3b-eadca26962db-14_360_1109_237_566}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a closed curve \(C\) with equation
$$r = 3 ( \cos 2 \theta ) ^ { \frac { 1 } { 2 } } , \quad \text { where } - \frac { \pi } { 4 } < \theta \leqslant \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } < \theta \leqslant \frac { 5 \pi } { 4 }$$
The lines \(P Q , S R , P S\) and \(Q R\) are tangents to \(C\), where \(P Q\) and \(S R\) are parallel to the initial line and \(P S\) and \(Q R\) are perpendicular to the initial line. The point \(O\) is the pole.
- Find the total area enclosed by the curve \(C\), shown unshaded inside the rectangle in Figure 1.
- Find the total area of the region bounded by the curve \(C\) and the four tangents, shown shaded in Figure 1.