(i) To find BD, use the formula for the perpendicular from the center to the chord: BD = 9\sin(\pi - 2.4). Calculating gives:

\(BD = 9\sin(\pi - 2.4) = 6.08 \text{ cm}\)

(ii) To find the perimeter of the shaded region, calculate the arc length AB and add the lengths of BD, OD, and OA:

Arc AB = 9 \times 2.4 = 21.6 \text{ cm}

Using Pythagoras or trigonometry, OD = 9\cos(\pi - 2.4) = 6.64 \text{ cm}

Perimeter = 21.6 + 6.08 + 9 + 6.64 = 43.3 \text{ cm}

(iii) To find the area of the shaded region, calculate the area of the sector and subtract the area of triangle OBD:

Area of sector = \(\frac{1}{2} \times 9^2 \times 2.4\)

Area of triangle OBD = \(\frac{1}{2} \times 6.08 \times 6.64\)

Total area = \(\frac{1}{2} \times 81 \times 2.4 - \frac{1}{2} \times 6.08 \times 6.64 = 117 \text{ cm}^2\)