How does one estimate the surface area of a threded object such as a bolt?
For a saw tooth thread - if you take the volume from the base of the thread and add it to the volume at the top of the thread and divide by 2, you should get the total volume.
In fact that would be a pretty close approximation for all threads, including this one. 
For the threaded part, you multiply by the secant of the taper angle. If that’s what it’s called - I hope somebody corrects me otherwise.
So for instance, if you had a cylinder with a radius of 8 mm and a length of 27 mm, the surface area on the side would be 2pi (8mm) (27mm) = 1357 mm[sup]2[/sup]. Now, if that cylinder were part of a bolt, tapered at, say, 51°, then you’d multiply by sec(51) = 1.589. Thus the surface area would be 2156 mm[sup]2[/sup].
Unless I’m mistaken, that will give you the volume of the protruding material that makes up the thread, not the surface area.
In longitudinal section, the surface of the thread looks like a ‘waveform’ - the troughs are the same shape as the peaks (that’s what I’m going to assume anyway).
I think you can safely assume that a slice of the bolt that includes one full ‘wave’ of thread will have a full 'wave all the way around (it will just start in the middle of a trough on one bit and the middle of a peak on another) and can be treated as if the thread were not helical, but was just a series of annular grooves, so the area of that section is going to be the length of the ‘wave’ surface, multiplied by the (average) circumference.
IANAMathematician though, so apply salt.
Oops, my ‘that’ was directed toward antechinus
Sorry - I am wrong. Thanks Mangetout. I was automatically started thinking volume instead of SA. Time for bed.