1. **State the problem:** Calculate the area of: i. the circle with radius $r=3.5$ cm, ii. the square $QPR$ inscribed in the circle, iii. the shaded region inside the circle but outside the square. 2. **Formulas and rules:** - Area of a circle: $$A_{circle} = \pi r^2$$ - Area of a square: $$A_{square} = s^2$$ where $s$ is the side length. - The square $QPR$ is inscribed in the circle, so its diagonal equals the diameter of the circle. - Diameter of circle: $$d = 2r = 7$$ cm. - For a square, diagonal $d$ and side $s$ relate by $$d = s\sqrt{2}$$. 3. **Calculate the area of the circle:** $$A_{circle} = \pi r^2 = 3.14 \times 3.5^2 = 3.14 \times 12.25 = 38.465$$ cm$^2$. 4. **Calculate the side length of the square:** $$s = \frac{d}{\sqrt{2}} = \frac{7}{\sqrt{2}} = \frac{7}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2}$$ 5. **Calculate the area of the square:** $$A_{square} = s^2 = \left(\frac{7\sqrt{2}}{2}\right)^2 = \frac{49 \times 2}{4} = \frac{98}{4} = 24.5$$ cm$^2$. 6. **Calculate the shaded region area:** The shaded region is the part of the circle outside the square. $$A_{shaded} = A_{circle} - A_{square} = 38.465 - 24.5 = 13.965$$ cm$^2$. **Final answers:** - Area of the circle: $38.465$ cm$^2$ - Area of the square $QPR$: $24.5$ cm$^2$ - Area of the shaded region: $13.965$ cm$^2$