Select the image in library, click on the top of the mask around the image. A long dialogue will show including cropped dimension (you need to have checked show grid extras and expanded view in the libary view options first). You can also go to view, view options and select what you want to show all the time in grid view, this includes showing cropped dimensions.
I mean getting cropped dimensions from the SDK API, for example with photo:getRawMetadata('cropdimensions')
local size = photo:getRawMetadata('croppedDimensions')
was the solution that Jeffrey Friedl kindly gave me.
I don't undestand why it is not on the SDK API information. Is there any additional source of information?
Victor's answer is correct. croppedDimensions was inadvertently left out of our documentation for the SDK.
I just checked the source code and it has been present as far back as Lightroom 2.0.