6.
\includegraphics[max width=\textwidth, alt={}, center]{ffa0b566-6448-491b-96d7-d3806bcfe063-3_684_1237_685_239} Triangle \(A B C\) has \(A B = 9 \mathrm {~cm} , B C 10 \mathrm {~cm}\) and \(C A = 5 \mathrm {~cm}\). A circle, centre \(A\) and radius 3 cm , intersects \(A B\) and \(A C\) at \(P\) and \(Q\) respectively, as shown in Fig. 2.

1. Show that, to 3 decimal places, \(\angle B A C = 1.504\) radians. Calculate,
2. the area, in \(\mathrm { cm } ^ { 2 }\), of the sector \(A P Q\),
3. the area, in \(\mathrm { cm } ^ { 2 }\), of the shaded region \(B P Q C\),
4. the perimeter, in cm , of the shaded region \(B P Q C\).