Or we could use 2*pi*r= the circumfrence of a circle. pi=22/7 r=whatever the arc is (13dme in the case above). Since an arc is a part of a circle, multiply above formula by the degrees in the arc over 360. This could be done on paper in maybe 20-30 secs and they may be impressed.

I hope my math is right as I haven't done a math course in years.