1. **State the problem:** Macsen's garden has a right triangle with base 14 m and height 16 m, and an inscribed circle with diameter 7 m. We need to find how many bags of gravel are needed to cover the shaded area, which is the area of the triangle minus the area of the circle. 2. **Calculate the area of the triangle:** The area of a triangle is given by the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Substitute the values: $$\text{Area}_{\triangle} = \frac{1}{2} \times 14 \times 16 = 7 \times 16 = 112 \text{ m}^2$$ 3. **Calculate the area of the circle:** The diameter of the circle is 7 m, so the radius $r$ is: $$r = \frac{7}{2} = 3.5 \text{ m}$$ The area of a circle is: $$\text{Area}_{circle} = \pi r^2 = \pi \times (3.5)^2 = \pi \times 12.25 = 12.25\pi \text{ m}^2$$ 4. **Calculate the shaded area:** The shaded area is the area of the triangle minus the area of the circle: $$\text{Area}_{shaded} = 112 - 12.25\pi$$ Using $\pi \approx 3.1416$: $$12.25 \times 3.1416 = 38.4846$$ So, $$\text{Area}_{shaded} = 112 - 38.4846 = 73.5154 \text{ m}^2$$ 5. **Calculate the number of bags of gravel needed:** Each bag covers 12.5 m$^2$. The number of bags needed is: $$\frac{73.5154}{12.5} = 5.8809$$ Since Macsen cannot buy a fraction of a bag, he needs to buy 6 bags. **Final answer:** Macsen needs 6 bags of gravel.