1. **State the problem:** We have a garden consisting of a rectangle 18.4 feet long and 8.6 feet wide, with two semi-circles on the shorter ends. We need to find: a) The area of one semi-circle. b) The total area of the garden. c) The total area converted to square metres. 2. **Formula and rules:** - Area of a circle: $$A = \pi r^2$$ - Area of a semi-circle: $$A = \frac{1}{2} \pi r^2$$ - Area of a rectangle: $$A = \text{length} \times \text{width}$$ - Conversion: $$1 \text{ foot} = 0.3048 \text{ metres}$$ so $$1 \text{ ft}^2 = (0.3048)^2 \text{ m}^2 = 0.092903 \text{ m}^2$$ 3. **Calculate the area of one semi-circle:** - Diameter of semi-circle = width of rectangle = 8.6 feet - Radius $$r = \frac{8.6}{2} = 4.3$$ feet - Area of one semi-circle: $$A = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (4.3)^2 = \frac{1}{2} \pi (18.49) = 9.245 \pi \approx 29.04$$ square feet 4. **Calculate the total area of the garden:** - Area of rectangle: $$18.4 \times 8.6 = 158.24$$ square feet - Area of two semi-circles = area of one circle with radius 4.3 feet: $$\pi (4.3)^2 = \pi (18.49) = 58.08$$ square feet - Total area: $$158.24 + 58.08 = 216.32$$ square feet 5. **Convert total area to square metres:** - Using conversion factor: $$216.32 \times 0.092903 = 20.10$$ square metres **Final answers:** - a) Area of one semi-circle = $$29.04$$ square feet - b) Total area of garden = $$216.32$$ square feet - c) Total area in square metres = $$20.10$$ square metres