The perimeter of a sector of a circle can be calculated by adding the arc length to twice the radius.

Given that the radius (\(r\)) is 8 cm and the angle (\(\theta\)) is 45 degrees, we need to find the arc length.

The formula for the arc length (\(s\)) of a sector with radius \(r\) and angle \(\theta\) in radians is:

\(s = r \cdot \theta\(

First, convert the angle from degrees to radians:

\(\theta = \frac{45 \pi}{180} = \frac{\pi}{4}\(

Now, calculate the arc length:

\(s = 8 \cdot \frac{\pi}{4} = 2\pi\(

The perimeter (\(P\)) of the sector is the sum of the arc length and twice the radius:

\(P = s + 2r = 2\pi + 2 \cdot 8 = 2\pi + 16\(