1. **Problem 12a: Calculate the shaded area of a square with an inscribed circle.** The square has side length $8$ m. The shaded area is the area of the square minus the area of the inscribed circle. 2. **Formulas:** - Area of square: $A_{square} = s^2$ - Area of circle: $A_{circle} = \pi r^2$ 3. **Calculate the area of the square:** $$A_{square} = 8^2 = 64 \text{ m}^2$$ 4. **Calculate the radius of the inscribed circle:** The circle is inscribed, so its diameter equals the side of the square. $$d = 8 \Rightarrow r = \frac{8}{2} = 4 \text{ m}$$ 5. **Calculate the area of the circle:** $$A_{circle} = \pi \times 4^2 = 16\pi \text{ m}^2$$ 6. **Calculate the shaded area:** $$A_{shaded} = A_{square} - A_{circle} = 64 - 16\pi \text{ m}^2$$ 7. **Approximate the shaded area:** Using $\pi \approx 3.1416$, $$A_{shaded} \approx 64 - 16 \times 3.1416 = 64 - 50.2656 = 13.7344 \text{ m}^2$$ --- **Final answer for 12a:** $$\boxed{64 - 16\pi \approx 13.73 \text{ m}^2}$$ --- **Note:** Since the user asked to solve step by step and only the first question (12a) is solved, the rest are ignored as per instructions.