The solution includes two distinct parts: logical propositions and geometric calculations. What was the original question?

$$
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}
$$

$$
\text{Area}_{\text{rectangle}} = 9 \text{ cm} \times 7 \text{ cm}
$$

$$
\text{Area}_{\text{rectangle}} = 63 \text{ cm}^2
$$
The area of the rectangle is $\boxed{63 \text{ cm}^2}$.

$$
\text{Area}_{\text{circle}} = \pi r^2
$$

$$
\text{Area}_{\text{circle}} = \frac{22}{7} \times (2.5 \text{ cm})^2
$$

$$
(2.5)^2 = 6.25
$$

$$
\text{Area}_{\text{circle}} = \frac{22}{7} \times 6.25 \text{ cm}^2
$$
$$
\text{Area}_{\text{circle}} = \frac{137.5}{7} \text{ cm}^2
$$
$$
\text{Area}_{\text{circle}} \approx 19.64 \text{ cm}^2
$$
The area of the circle is $\boxed{19.64 \text{ cm}^2}$.

$$
\text{Area}_{\text{shaded}} = \text{Area}_{\text{rectangle}} - \text{Area}_{\text{circle}}
$$

$$
\text{Area}_{\text{shaded}} = 63 \text{ cm}^2 - \frac{137.5}{7} \text{ cm}^2
$$

$$
\text{Area}_{\text{shaded}} = \frac{63 \times 7 - 137.5}{7} \text{ cm}^2
$$
$$
\text{Area}_{\text{shaded}} = \frac{441 - 137.5}{7} \text{ cm}^2
$$
$$
\text{Area}_{\text{shaded}} = \frac{303.5}{7} \text{ cm}^2
$$
$$
\text{Area}_{\text{shaded}} \approx 43.36 \text{ cm}^2
$$
The area of the shaded region is $\boxed{43.36 \text{ cm}^2}$.