1. Given: OS = 7 cm and R is the midpoint of OS, so OR = RS = 3.5 cm. 2. (a) Diameter of OS: Since OS is a radius, diameter = 2 \times OS = 2 \times 7 = 14 cm. 3. (b) Perimeter of sector OSR includes two radii and arc OSR. - Radius OR = 3.5 cm (half OS) - Arc length of sector OSR = \frac{\theta}{360} \times 2 \pi r = \frac{40}{360} \times 2 \times \frac{22}{7} \times 3.5. Calculate arc length: $$\frac{40}{360} \times 2 \times \frac{22}{7} \times 3.5 = \frac{1}{9} \times 2 \times 11 = \frac{22}{9} \approx 2.44 \text{ cm}.$$ - Perimeter = OR + RS + arc length = 3.5 + 3.5 + 2.44 = 9.44 cm. 4. (c) Area of shaded region (sector OST) = total sector OS area - area of ORU: - Area of sector OS (radius 7 cm, angle 40°): $$\frac{40}{360} \times \pi \times 7^2 = \frac{1}{9} \times \pi \times 49 = \frac{49 \pi}{9}.$$ Using \( \pi = \frac{22}{7} \), area = \(\frac{49 \times 22}{9 \times 7} = \frac{49 \times 22}{63} = \frac{1078}{63} \approx 17.11 \text{ cm}^2.\) - Area of unshaded region ORU (radius 3.5 cm, angle 40°) given: $$\frac{40}{360} \times \pi \times (3.5)^2 = \frac{22}{9} \approx 2.44 \text{ cm}^2.$$ - Therefore, shaded area = area sector OS - area ORU = 17.11 - 2.44 = 14.67 cm². 5. Final answers rounded to two decimal places: (a) Diameter = 14.00 cm (b) Perimeter = 9.44 cm (c) Area of shaded region = 14.67 cm²