The area of a circular sector is given by:
![A=(\theta)/(360)\pi r^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/k2egk4cxo2hfakmvs91396oky0hblwcnf6.png)
In this case each shaded part has an angle of 136°, this means that the total circular sector has a total angle of 272°, plugging this value and the value of the radius into the equation above we have:
![A=(272)/(360)\pi(18)^2=769.06](https://img.qammunity.org/2023/formulas/mathematics/college/ov0m0vbew04kl6fm3pmz6t7mp1fm4khv2m.png)
Therefore the area of the shaded region is 769.06 squared cm and the answer is C.