1. **State the problem:** We have a circular parlor with radius $r=4$ cm (distance from door to middle). A circular table in the middle occupies 10% of the parlor's area. We want to find the area of the table's shadow, but only half of the shadow is visible (the other half is obstructed). 2. **Formula for area of a circle:** $$A = \pi r^2$$ where $r$ is the radius. 3. **Calculate the area of the parlor:** $$A_{parlor} = \pi \times 4^2 = 16\pi$$ cm$^2$ 4. **Calculate the area of the table:** The table takes 10% of the parlor's area: $$A_{table} = 0.10 \times 16\pi = 1.6\pi$$ cm$^2$ 5. **Calculate the visible shadow area:** Half of the table's shadow is obstructed, so visible shadow area is half of the table's area: $$A_{shadow} = \frac{1}{2} \times 1.6\pi = 0.8\pi$$ cm$^2$ 6. **Final answer:** $$A_{shadow} \approx 0.8 \times 3.1416 = 2.5133$$ cm$^2$ So, the visible area of the table's shadow is approximately 2.51 cm$^2$.