SEM is not a good technique to quantify surface area. It can give you some idea of surface morphology, but cannot give you "bulk" pore information. You will need to perform porosimetry. In addition to mercury porosimtery, you can also do nitrogen porosimetry (much less toxic!). It can also be done with other gases, but nitrogen is most commonly used. Here is an example of a gas porosimeter:
I think that surface area is calculated by SEM technique is not good method. Generally, method for calculating surface area of materials often use BET technique. I recommend it.
You could also use the argon adsorption with DFT equation at 87 K (- 186 °C). The pore range is between 0.4 to 100 nm. With this method, you could have the surface area and the pore volume versus the pore size. You could check in this journal article. They give some details about this technique.
The mercury porosimeter is a very good technique but when you want to measure the surface area in nanopores, the pressure is really high and you could destroy the pore structure.
The only way you can do it, is if your particle are non-porous.
Since SEM cannot see micropores, in non-porous particles you can estimate the size distribution from a few images and then assuming the geometry for calculating the area.
This is shown clearly in the classical Gregg&Sing book, where if you have non-porous cubes of side length L and density r, the area is A=6/rL