Side, area and perimeter of a quadrilateral split by a diagonal, and bearings between its vertices

The diagram shows the positions of four villages, \(P\), \(Q\), \(R\) and \(S\), on horizontal ground, forming the quadrilateral \(PQRS\). The diagonal \(QS\) is drawn. It is given that \(PQ=9\text{ km}\), \(PS=6\text{ km}\), \(\angle QPS=70^\circ\), \(\angle QRS=65^\circ\) and \(\angle RQS=40^\circ\).

1. Find the length of \(QR\).[4]
2. Find the area of the quadrilateral \(PQRS\).[3]
3. Find the perimeter of the quadrilateral \(PQRS\).[4]
4. The bearing of \(S\) from \(Q\) is \(075^\circ\).
   Find the bearing of \(P\) from \(Q\).[3]
5. Find the bearing of \(Q\) from \(P\).[2]