(a) To find the perimeter of the shaded region, we first find the angle \(\angle APQ\) using the cosine rule:

\(\cos^{-1} \left( \frac{5}{6} \right) = 0.5857 \text{ radians}\)

The perimeter of the shaded region is given by:

\(4 \times r \times 0.5857 = 2.34r\)

Alternatively, it can be expressed as \(0.745\pi r\) or \(\frac{293}{125}r\).

(b) To find the area of the shaded region, we use the sector formula for \(\text{Sector APB}\):

\(\frac{1}{2}r^2 \times (2 \times 0.5857)\)

Using the appropriate formula for the area of a triangle and combining it with the sector, we find:

\(\text{Shaded area} = 0.250r^2\)

Alternatively, it can be expressed as \(0.0796\pi r^2\).