(a) The area of triangle ABC can be calculated using the formula for the area of a triangle: \(\frac{1}{2} r^2 \sin(2θ)\).

The area of sector ABD is \(\frac{1}{2} r^2 θ\).

Therefore, the area of the shaded region is the area of triangle ABC minus the area of sector ABD: \(\frac{1}{2} r^2 \sin(2θ) - \frac{1}{2} r^2 θ = \frac{1}{2} r^2 (\sin 2θ - θ)\).

(b) The arc BD is given by \(rθ = 10 \times 0.6 = 6\) cm.

The length AC is \(2r \cos θ = 2 \times 10 \times \cos 0.6 = 16.506\) cm.

The length DC is \(AC - r = 16.506 - 10 = 6.506\) cm.

The perimeter of the shaded region is the sum of the arc BD, and the lengths DC and CD: \(6 + 6.506 + 10 = 22.5\) cm.