1. **State the problem:** We are given two sectors of circles with given radii and central angles. We need to find the perimeter and area of the shaded regions for each sector, taking \(\pi = \frac{22}{7}\). --- ### Part (a): Radius \(r=21\) cm (Angle not given explicitly, so we assume the entire sector is a semicircle or find using available info.) Since angle is not directly provided, we assume it is the full semicircle (180°) or we must find it based on the problem's original diagram if available. Given only radius 21 cm, let's find formulas to use when angle \(\theta\) is given. The formulas for a sector: - Arc length \(L = r\theta\) when \(\theta\) is in radians. - Area \(A = \frac{1}{2}r^{2} \theta\) - Perimeter \(P = L + 2r\) If no angle is specified, we cannot find numeric answers. So we proceed to part (c) which has an explicit angle. --- ### Part (c): Radius \(r=35\) cm, angle \(\theta=30^\circ\) 2. **Convert angle to radians:** $$\theta = 30^\circ = \frac{30 \pi}{180} = \frac{\pi}{6}$$ 3. **Calculate arc length:** $$L = r\theta = 35 \times \frac{\pi}{6} = 35 \times \frac{22}{7} \times \frac{1}{6} = 35 \times \frac{22}{42} = 35 \times \frac{11}{21} = \frac{385}{21} = 18.33\text{ cm (approx)}$$ 4. **Calculate perimeter of shaded sector:** $$P = \text{arc length} + 2r = 18.33 + 2 \times 35 = 18.33 + 70 = 88.33 \text{ cm}$$ 5. **Calculate area of shaded sector:** $$A = \frac{1}{2} r^2 \theta = \frac{1}{2} \times 35^2 \times \frac{\pi}{6} = \frac{1}{2} \times 1225 \times \frac{22}{7} \times \frac{1}{6} = 612.5 \times \frac{22}{42} = 612.5 \times \frac{11}{21} = \frac{6737.5}{21} = 320.83 \text{ cm}^2 \text{ (approx)}$$ --- **Final answers:** - **Part (a):** Insufficient information to determine area and perimeter due to missing angle. - **Part (c):** - Perimeter \(P \approx 88.33\) cm - Area \(A \approx 320.83\) cm\(^2\)