+885 Hello! Let's say we have an arc, and its measure is 36 degrees. If we know that one side length is 10 units what is the perimeter of the arc?
+129852 Ant....I assume that we have a decagon [ regular polygon of 10 sides ] inscribed in a circle??......if so....
The radius, r, of the circle can be found as
r / sin 72 = 10/ sin 36
r = 10sin72 / sin 36 = 5 (1 + √5 )
So....the perimeter of the arc [ arc length of 1/10 of the circle ] is
2pi r / 10 =
2pi [ 5 ( 1 + √5)] / 10 = pi * (1 + √5) units ≈ 10.17 units
+129852 Oh, OK....the radius = 10
Arc length = arc length of whole circle * (36/360) =
2pi (radius) * (36/360) =
2pi (10) * (1/10 ) =
2pi units ≈ 6.28 units
+118673 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 \(10\pi+10+10 = 20+10\pi\;\;units\)
-----------------------
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.
+129852 Ah...I see....Ant wanted the perimeter of the sector.....!!!
This should be
Sum of radii + arc we found
10 + 10 + 2pi = [20 + 2pi ] = 26.28 units
And you are correct, Ant....
+129852 I think you made a slight error, Melody
You computed (1/10) of the area of the circle...not (1/10) of the circumference
Kind of looks like this!
