Question

what is the length of arc PQ? What is the area of the shaded region?

Answer 1

Comment
I'm assuming you mean the minor arc. That's the part of the circumference that is in the shaded part.

Part One
The length of the arc is connected to the central angle which you are given as 155o
r = 9 in
The arc length = $\theta*r * 2\pi /360$
Since $\theta$= 155 degrees

The arc length = 2*3.14 * 9*155 / 360
The arc length = 24.3 inches

The sector area = (central angle/360) * pi * r^2 .
The sector area = (155/360) * 3.14 * 9^2
The sector area = 109.5 in^2

Answers
Arc length = 24.3  <<<<<<< answer
Arc area = 109.5 <<<<<<<<answer