1. **State the problem:** We need to find the area of the curved region (a segment of a circle) given the radius of curvature and the sagitta (height) of the arc. 2. **Given data:** - Radius of curvature $R = 230$ m - Sagitta (height) $h = 100$ m - Chord length $c = 200$ m 3. **Formula for the area of a circular segment:** $$\text{Area} = R^2 \arccos\left(\frac{R - h}{R}\right) - (R - h) \sqrt{2Rh - h^2}$$ 4. **Calculate intermediate values:** - Calculate $\frac{R - h}{R} = \frac{230 - 100}{230} = \frac{130}{230} = \frac{13}{23}$ - Calculate $\arccos\left(\frac{13}{23}\right)$ (in radians). Using a calculator, $\arccos\left(\frac{13}{23}\right) \approx 1.000$ radians - Calculate $\sqrt{2Rh - h^2} = \sqrt{2 \times 230 \times 100 - 100^2} = \sqrt{46000 - 10000} = \sqrt{36000} = 189.7367$ m 5. **Calculate the area:** $$\text{Area} = 230^2 \times 1.000 - 130 \times 189.7367 = 52900 - 24665.77 = 28234.23 \text{ m}^2$$ 6. **Interpretation:** The area of the curved segment is approximately $28234.23$ square meters. **Final answer:** $$\boxed{28234.23 \text{ m}^2}$$