1. Problem (a): Find the area of grass in a rectangular park 50m by 40m with a 3m flower bed around two longer sides and one short side, and a circular fish pond of diameter 8m in the center. 2. Formula for area of rectangle: $$\text{Area} = \text{length} \times \text{width}$$ 3. Formula for area of circle: $$\text{Area} = \pi r^2$$ 4. Calculate total park area: $$50 \times 40 = 2000\,m^2$$ 5. Calculate flower bed area: The flower bed covers two longer sides (50m) and one short side (40m) with width 3m. 6. The flower bed forms a shape extending 3m along these sides. The flower bed area can be found by subtracting the inner rectangle (excluding flower bed) from the total park area. 7. Inner rectangle dimensions: length = 50m - 2 \times 3m = 44m (since flower bed on two longer sides), width = 40m - 3m = 37m (flower bed on one short side only). 8. Inner rectangle area: $$44 \times 37 = 1628\,m^2$$ 9. Flower bed area: $$2000 - 1628 = 372\,m^2$$ 10. Fish pond area: diameter = 8m, radius $$r = \frac{8}{2} = 4m$$ 11. Fish pond area: $$\pi \times 4^2 = 16\pi \approx 50.27\,m^2$$ 12. Area to be grassed = inner rectangle area minus fish pond area: $$1628 - 50.27 = 1577.73\,m^2$$ 13. Rounded to nearest square metre: $$1578\,m^2$$ 14. Problem (b): Find area of sector of circle with radius 35mm and central angle 75º. 15. Formula for sector area: $$\text{Area} = \frac{\theta}{360} \times \pi r^2$$ where $$\theta$$ is angle in degrees. 16. Calculate sector area: $$\frac{75}{360} \times \pi \times 35^2 = \frac{75}{360} \times \pi \times 1225$$ 17. Simplify: $$= 0.2083 \times 3.1416 \times 1225 \approx 801.1\,mm^2$$ 18. Rounded to nearest square millimetre: $$801\,mm^2$$