1. **Problem (a):** Find the area of grass in a rectangular park measuring 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. **Step 1:** Calculate the total area of the park. $$\text{Area}_{\text{park}} = 50 \times 40 = 2000\ \text{m}^2$$ 3. **Step 2:** Calculate the area covered by the flower bed. - The flower bed is 3m wide around two longer sides (50m) and one short side (40m). - The flower bed forms an L-shape around these sides. - The flower bed area can be found by subtracting the inner rectangle (excluding flower bed) from the total area of the park extended by the flower bed on those sides. 4. **Step 3:** Dimensions of the inner rectangle excluding flower bed: - Length remains 50m (flower bed only on two longer sides, so width changes) - Width reduces by 3m on one short side only, so inner width = 40 - 3 = 37m 5. **Step 4:** Calculate the area of the flower bed: $$\text{Area}_{\text{flower bed}} = \text{Area}_{\text{park}} - (50 \times 37) = 2000 - 1850 = 150\ \text{m}^2$$ 6. **Step 5:** Calculate the area of the circular fish pond. - Diameter = 8m, so radius $r = \frac{8}{2} = 4$ m - Area of pond: $$\text{Area}_{\text{pond}} = \pi r^2 = \pi \times 4^2 = 16\pi \approx 50.27\ \text{m}^2$$ 7. **Step 6:** Calculate the area to be grassed. $$\text{Area}_{\text{grass}} = \text{Area}_{\text{park}} - \text{Area}_{\text{flower bed}} - \text{Area}_{\text{pond}} = 2000 - 150 - 50.27 = 1799.73\ \text{m}^2$$ 8. **Step 7:** Round to nearest square metre. $$\boxed{1800\ \text{m}^2}$$ --- 9. **Problem (b):** Find the area of a sector of a circle with radius 35mm and central angle 75°. 10. **Step 1:** Use the formula for sector area: $$\text{Area}_{\text{sector}} = \frac{\theta}{360} \times \pi r^2$$ where $\theta = 75^\circ$, $r = 35$ mm. 11. **Step 2:** Calculate the area: $$\text{Area}_{\text{sector}} = \frac{75}{360} \times \pi \times 35^2 = \frac{75}{360} \times \pi \times 1225$$ 12. **Step 3:** Simplify: $$= \frac{75}{360} \times 3.1416 \times 1225 \approx 0.2083 \times 3.1416 \times 1225$$ $$\approx 0.2083 \times 3848.45 = 801.76\ \text{mm}^2$$ 13. **Step 4:** Round to nearest square millimetre: $$\boxed{802\ \text{mm}^2}$$