1. **State the problem:** We need to find the area of a composite figure consisting of a rectangle on top of a semicircle. 2. **Identify the dimensions:** - Rectangle width = 5 mm - Rectangle height = 7 mm - Semicircle radius = 9 mm 3. **Formula for area:** - Area of rectangle = width \times height - Area of semicircle = \frac{1}{2} \pi r^2 4. **Calculate the area of the rectangle:** $$\text{Area}_{rectangle} = 5 \times 7 = 35 \text{ mm}^2$$ 5. **Calculate the area of the semicircle:** $$\text{Area}_{semicircle} = \frac{1}{2} \pi (9)^2 = \frac{1}{2} \pi \times 81 = 40.5 \pi \text{ mm}^2$$ 6. **Approximate the semicircle area:** $$40.5 \pi \approx 40.5 \times 3.1416 = 127.23 \text{ mm}^2$$ 7. **Total area of the figure:** $$\text{Area}_{total} = 35 + 127.23 = 162.23 \text{ mm}^2$$ **Final answer:** The area of the figure is approximately **162.23 square millimeters**.