L2 
4pA-kA2
k = 1/R2
for sphere, k < 0 for hyperbolic
plane
Spherical planimeter, Jacob Amsler, 1884
Check eBay for planimeters!
References
Two survey articles on isoperimetric inequalities by R.
Osserman
BAMS, Nov. 1978
Monthly, Jan. 1979
Recent results on the isoperimetric problem on general
surfaces
Frank Morgan, et.al., Monthly, May 1999
My planimeter web page
http://persweb.wabash.edu/facstaff/footer/Planimeter/PLANIMETER.HTM
or
www.wabash.edu and look for math dept page