Using the 1 hex equals 1 parsec definition, one sector is 4,096 square parsecs and so the entire 3rd Imperium is roughly 20 sectors x 4096 or 81,920 square parsecs?

A parsec being 3.26 light years, then the Imperium occupies about 267,000 square light years.

Is there a canon definition of the size of the Imperium beyond that it contains 11,000 worlds?