Thanks CPhill, since you are not here, and ant101 has asked for clarifictaion, I will add my input.
Hi Ant101
There are 360 degrees in a circle
so 36 degrees is one tenth of a circle and the radius of your circle is 10
so the arc length is \(\text{one tenth }*\pi*10^2 = 0.1*\pi*100=10\pi\)
NOW, your question is worded incorrectly and technically it does not make sense.
An arc is a part of a circle's circumference and it does not have a perimeter because it is not a closed curve.
An arc has a length, which I have alredy found for you.
I think you are actually asking for the perimeter of the sector.
A sector is a part of a circle which includes 2 radii and the arc between them.
For instance, when you cut a cake you usually cut it into sectors.
so
The perimeter of the sector is \(10\pi+10+10 = 20+10\pi\;\;units\)
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My answer is very different from CPhill's. This is because the question is worded incorrectly and he interpreted its meaning very differently from me.