6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{893efbc9-8321-469f-bd5e-89f9d5827737-09_650_937_269_482}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve \(C\) shown in Figure 1 has polar equation
$$r = 2 + \cos \theta , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$
At the point \(A\) on \(C\), the value of \(r\) is \(\frac { 5 } { 2 }\).
The point \(N\) lies on the initial line and \(A N\) is perpendicular to the initial line.
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve \(C\), the initial line and the line \(A N\).
Find the exact area of the shaded region \(R\).