<u>Given</u>:
The radius of the circle is 12 units.
The central angle of the shaded region is 90°
We need to determine the arc length of the shaded region.
<u>Arc length:</u>
The arc length of the shaded region can be determined using the formula,
![Arc \ length=(\frac{\theta}{360} ) 2 \pi r](https://tex.z-dn.net/?f=Arc%20%5C%20length%3D%28%5Cfrac%7B%5Ctheta%7D%7B360%7D%20%29%202%20%5Cpi%20r)
substituting
and r = 12, we get;
![Arc \ length=(\frac{90}{360} ) 2 (3.14)(12)](https://tex.z-dn.net/?f=Arc%20%5C%20length%3D%28%5Cfrac%7B90%7D%7B360%7D%20%29%202%20%283.14%29%2812%29)
Multiplying the terms, we have;
![Arc \ length=\frac{6782.4}{360}](https://tex.z-dn.net/?f=Arc%20%5C%20length%3D%5Cfrac%7B6782.4%7D%7B360%7D)
Dividing, we get;
![Arc \ length=18.84](https://tex.z-dn.net/?f=Arc%20%5C%20length%3D18.84)
Rounding off to the nearest tenth, we get;
![Arc \ length =18.8](https://tex.z-dn.net/?f=Arc%20%5C%20length%20%3D18.8)
Thus, the arc length of the shaded region is 18.8 units.