Most CAD software has an "analyze" function or maybe "Properties" that will list perimeter, surface area and if the part is 3D it will tell you volume and can give weights based on the type of material. You should be able to get the perimeter pretty easily that way. If nothing else, dimension all the straight lines and add the numbers up, it should be pretty close.
Brian Lamb
Lamb Tool Works, Custom tools for woodworkers
Equipment: Felder KF700 and AD741, Milltronics CNC Mill, Universal Laser X-600