1. Problem (a): Complete the pseudo code to calculate the area of a sector with radius $r$ and angle $\theta$. The formula for the area of a sector is $$\text{Area} = \frac{\theta}{360} \times \pi r^2$$ where $\theta$ is in degrees. 2. Pseudo code completion: - Input radius $r$ - Input angle $\theta$ - Calculate area as $\text{Area} = \frac{\theta}{360} \times 3.1416 \times r \times r$ - Output area 3. Problem (b): The scale of the map is 1:20,000, meaning 1 unit on the map represents 20,000 units in reality. 4. Actual area of residential plots is 50 km$^2$. Convert this to cm$^2$: - 1 km = 100,000 cm, so - $50 \text{ km}^2 = 50 \times (100,000)^2 = 50 \times 10^{10} = 5 \times 10^{11}$ cm$^2$ 5. Area on the map is scaled down by the square of the scale factor: - Scale factor = 20,000 - Area on map = $\frac{\text{Actual area}}{(20,000)^2} = \frac{5 \times 10^{11}}{4 \times 10^{8}} = 1250$ cm$^2$ 6. Final answers: - (a) Area of sector = $\frac{\theta}{360} \times \pi r^2$ - (b) Area of residential plot on map = 1250 cm$^2$