1. **Problem Statement:** Calculate the areas of: i) The circle with radius $r=3.5$ cm. ii) The square $QPQR$ inscribed in the circle. iii) The shaded region (area of the circle minus area of 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. - For a square inscribed in a circle, the diagonal of the square equals the diameter of the circle. 3. **Calculations:** i) Area of the circle: $$A_{circle} = \pi \times (3.5)^2 = \pi \times 12.25 = 3.14 \times 12.25 = 38.465$$ cm$^2$ ii) Side length of the square: - Diameter of circle = $2 \times 3.5 = 7$ cm - Diagonal of square $d = 7$ cm - Side length $s$ of square satisfies: $$s = \frac{d}{\sqrt{2}} = \frac{7}{\sqrt{2}} = \frac{7}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2}$$ 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$^2$ iii) Area of the shaded region: $$A_{shaded} = A_{circle} - A_{square} = 38.465 - 24.5 = 13.965$$ cm$^2$ 4. **Final answers:** - Area of the circle: $38.465$ cm$^2$ - Area of the square $QPQR$: $24.5$ cm$^2$ - Area of the shaded region: $13.965$ cm$^2$