3.3: Concentric sectors and three shaded segments

The diagram shows sectors $AOB$ and $COD$ of two circles with the same centre, $O$. Angle $AOB$ is $\dfrac{3\pi}{8}$ and the length of $OC$ is $6.5$. It is given that $OAC$ and $OBD$ are straight lines and $OA:OC$ is $4:5$. Find the perimeter of the shaded region.

The diagram shows a circle with centre $O$ and radius $a$. Sector $PQR$ is a sector of a different circle with centre $R$ and radius $y$. Angle $OPR$ is $\phi$. Find, in terms of $a$ and $\phi$ only, the total area of the three shaded regions. Simplify your answer.