1. **Problem statement:** ABCD is a square with side length 9 cm. Inside it, a circle is inscribed touching all sides. Find the shaded area, which is the area of the square minus the area of the circle. 2. **Formulas and rules:** - Area of square: $A_{square} = s^2$ where $s$ is the side length. - Area of circle: $A_{circle} = \pi r^2$ where $r$ is the radius. - For a circle inscribed in a square, the diameter equals the side length, so $d = s$ and $r = \frac{s}{2}$. 3. **Calculate the area of the square:** $$A_{square} = 9^2 = 81$$ 4. **Calculate the radius of the circle:** $$r = \frac{9}{2} = 4.5$$ 5. **Calculate the area of the circle:** $$A_{circle} = 3.14 \times (4.5)^2 = 3.14 \times 20.25 = 63.585$$ 6. **Calculate the shaded area:** $$A_{shaded} = A_{square} - A_{circle} = 81 - 63.585 = 17.415$$ 7. **Final answer:** The shaded area is approximately **17.415 cm²**.