Answer:
8.5pi
Step-by-step explanation:
We can solve this problem with a rule of three.
The area of the whole circle is represented by a sector with central angle of 2*pi. So, if we want to find the area of a sector that has a central angle of 17pi/9, we can use the following logic:
sector of 2pi -> area equal to 9pi
sector of 17pi/9 -> area equal to X
2pi / (17pi/9) = 9pi / X
18 / 17 = 9pi / X
X = 17 * 9pi / 18 = 17pi / 2 = 8.5pi
