1. **State the problem:** Find the area of the curved segment of a circle given the radius of curvature $R=100$ m and sagitta (height) $h=100$ m. 2. **Given data:** - Radius of curvature $R=100$ - Sagitta $h=100$ 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 $\frac{R - h}{R} = \frac{100 - 100}{100} = 0$ - Calculate $\arccos(0) = \frac{\pi}{2} \approx 1.5708$ radians - Calculate $\sqrt{2 \times 100 \times 100 - 100^2} = \sqrt{20000 - 10000} = \sqrt{10000} = 100$ 5. **Calculate the area:** $$\text{Area} = 100^2 \times 1.5708 - 0 \times 100 = 10000 \times 1.5708 = 15708$$ 6. **Interpretation:** The area of the curved segment is approximately $15708$ square meters. **Final answer:** $$\boxed{15708}$$