As the otolith shape is species-specific, otolith area (surface?) and perimeter depend very much on the species you are dealing with. I would suggest that you examine otoliths of specimens of different sizes for your species of interest, and measure the values you are interested in. Then, for example, you can plot otolith perimeter against standard length of the fish or maximum otolith length, and get a function that you can use to estimate those values.
To estimates the surface and perimeter of an otolith, you can use imageJ (https://imagej.nih.gov/ij/) that is an open source free software that do it easily. Just bear in mind that due to the irregular shape of otolith from som species, you really have to take care of the position of the otolith. It is also very useful to use ratio when looking at relationship between otolith size and total lenght of a fish. Some more sophisticate software linked to numerical microscope (Keyance for example) aloow you to reconstruct a 3D image of your otolith where you can do every kind of measure you want afterward.
If you can take good pictures of the otoliths you are interested in, ImageJ (available freely at http://rsb.info.nih.gov/ij/download.html) will allow you to calibrate these images (= how many mm represent X pixels on each image), semi-automatically obtain the projected 2D area and the perimeter of each otolith.
Depending on the shape of the otoliths, I suggest using some plasticine for keeping the otoliths in the same position.
Do not hesitate to contact me directly if something is not clear.
I use Image Processing Toolkit to automatically measure lengths, circumferences and areas of all objects in an image. That package isn't being sold any longer but more expensive ones are.