11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e116a86f-63e0-4e80-b49c-d9f3c819ce15-28_451_899_239_584}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows the design of a badge.
The shape \(A B C O A\) is a semicircle with centre \(O\) and diameter 10 cm .
\(O B\) is the arc of a circle with centre \(A\) and radius 5 cm .
The region \(R\), shown shaded in Figure 4, is bounded by the arc \(O B\), the arc \(B C\) and the line \(O C\).
Find the exact area of \(R\).
Give your answer in the form \(( a \sqrt { 3 } + b \pi ) \mathrm { cm } ^ { 2 }\), where \(a\) and \(b\) are rational numbers.