1. **State the problem:** Calculate the shaded area in the semicircle diagram where the radius $r=25$ cm and $OM=18$ cm. 2. **Identify the shaded area:** The shaded area is the segment of the circle cut off by chord $AB$. 3. **Formula for segment area:** The area of a segment is given by $$\text{Segment area} = \text{Sector area} - \text{Triangle area}$$ 4. **Calculate the sector area:** The sector angle $\angle AOB$ was found to be $87.9^\circ$. Convert to radians: $$\theta = 87.9^\circ \times \frac{\pi}{180} = 1.534 \text{ radians}$$ Sector area: $$\text{Sector area} = \frac{1}{2} r^2 \theta = \frac{1}{2} \times 25^2 \times 1.534 = \frac{1}{2} \times 625 \times 1.534 = 478.125 \text{ cm}^2$$ 5. **Calculate the triangle area:** Triangle $OAB$ is isosceles with sides $OA=OB=25$ cm and angle $87.9^\circ$ between them. Triangle area formula: $$\text{Area} = \frac{1}{2} ab \sin C$$ where $a=b=25$ cm and $C=87.9^\circ$. Calculate: $$\sin 87.9^\circ \approx 0.999$$ $$\text{Triangle area} = \frac{1}{2} \times 25 \times 25 \times 0.999 = 312.375 \text{ cm}^2$$ 6. **Calculate the shaded segment area:** $$\text{Shaded area} = 478.125 - 312.375 = 165.75 \text{ cm}^2$$ 7. **Final answer:** Rounded to nearest whole number, $$\boxed{166 \text{ cm}^2}$$