1. **Stating the problem:** Encik Hamid wants to plant 18 oil palm trees arranged so that the distance between each tree is 9 m, and the planting pattern forms an equilateral triangle grid. We need to find the total area of the land used. 2. **Understanding the arrangement:** In an equilateral triangle lattice, trees are planted at the vertices of equilateral triangles with side length $s=9$ m. 3. **Number of trees and rows:** The trees form a triangular number pattern. The total number of trees $T$ in $n$ rows is given by: $$T = \frac{n(n+1)}{2}$$ We know $T=18$, so solve for $n$: $$\frac{n(n+1)}{2} = 18 \implies n(n+1) = 36$$ Try integer values: - For $n=5$, $5\times6=30$ (too small) - For $n=6$, $6\times7=42$ (too large) Since 18 is not a triangular number, the planting might be arranged in a nearly triangular pattern. However, the closest triangular number less than 18 is 15 (for $n=5$), and the next is 21 (for $n=6$). Assuming the planting forms a triangle with 6 rows (21 trees), but only 18 trees are planted, the area corresponds to 6 rows. 4. **Calculating the height of the triangular planting area:** The height $h$ of an equilateral triangle with side length $s$ is: $$h = \frac{\sqrt{3}}{2} s = \frac{\sqrt{3}}{2} \times 9 = \frac{9\sqrt{3}}{2}$$ 5. **Total height of the planting area:** Since there are $n=6$ rows, the total height is: $$H = (n-1) \times h = 5 \times \frac{9\sqrt{3}}{2} = \frac{45\sqrt{3}}{2}$$ 6. **Base length of the planting area:** The base has $n=6$ trees spaced 9 m apart, so the base length is: $$B = (n-1) \times s = 5 \times 9 = 45$$ 7. **Area of the triangular land:** $$\text{Area} = \frac{1}{2} \times B \times H = \frac{1}{2} \times 45 \times \frac{45\sqrt{3}}{2} = \frac{45 \times 45 \sqrt{3}}{4} = \frac{2025\sqrt{3}}{4}$$ 8. **Final answer:** $$\boxed{\text{Area} = \frac{2025\sqrt{3}}{4} \approx 875.44 \text{ square meters}}$$ This is the approximate area of the land needed to plant 18 oil palm trees in an equilateral triangle pattern with 9 m spacing.