1. **Problem statement:** Find the area of the shaded quarter circle inside a square with side length 7 cm. 2. **Formula used:** The area of a quarter circle is given by $$\text{Area} = \frac{1}{4} \pi r^2$$ where $r$ is the radius of the circle. 3. **Given:** Radius $r = 7$ cm. 4. **Calculate the area:** $$\text{Area} = \frac{1}{4} \pi (7)^2 = \frac{1}{4} \pi \times 49 = \frac{49}{4} \pi$$ 5. **Approximate using $\pi \approx 3.14$:** $$\text{Area} \approx \frac{49}{4} \times 3.14 = 12.25 \times 3.14 = 38.465$$ 6. **Interpretation:** The area of the quarter circle is approximately 38.47 cm². 7. **Check options:** None of the options (115.5, 201.5, 315.5, 405.5 cm²) match this area, so the question might be about the area of the square minus the quarter circle or another shape. 8. **Calculate area of the square:** $$\text{Area}_{square} = 7 \times 7 = 49 \text{ cm}^2$$ 9. **Calculate area of the shaded region (square minus quarter circle):** $$49 - 38.465 = 10.535 \text{ cm}^2$$ 10. **This also does not match the options, so likely the problem is about the quarter circle area multiplied or scaled.** Since the user only asked for the answer and method for the first problem, we provide the quarter circle area as above. **Final answer:** The area of the quarter circle is approximately $38.47$ cm², which does not match the given options exactly. --- **Note:** The second problem is not solved as per instructions.