1. **Problem statement:** We need to find the area of the shaded segment of a circle. The sector has radius $r=16$ cm and central angle $\theta=140.3^\circ$. The chord length is 30.1 cm and the height of the segment (distance from chord to arc) is 5.4 cm. 2. **Formula for segment area:** The area of a segment is the area of the sector minus the area of the triangle formed by the two radii and the chord. 3. **Calculate the sector area:** $$\text{Sector area} = \frac{\theta}{360} \times \pi r^2 = \frac{140.3}{360} \times \pi \times 16^2$$ 4. **Calculate the triangle area:** The triangle formed is isosceles with two sides $r=16$ cm and base equal to the chord $c=30.1$ cm. We can also use the height $h=5.4$ cm to find the triangle area: $$\text{Triangle area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 30.1 \times 5.4$$ 5. **Calculate each area numerically:** $$\text{Sector area} = \frac{140.3}{360} \times \pi \times 256 = 0.3897 \times 3.1416 \times 256 = 313.3 \text{ cm}^2$$ $$\text{Triangle area} = 0.5 \times 30.1 \times 5.4 = 81.3 \text{ cm}^2$$ 6. **Calculate the segment area:** $$\text{Segment area} = \text{Sector area} - \text{Triangle area} = 313.3 - 81.3 = 232.0 \text{ cm}^2$$ 7. **Final answer:** The area of the shaded segment is $\boxed{232.0}$ cm$^2$ to 1 decimal place.