A Center Controller reported they received a handoff from the adjacent TRACON sector of an aircraft that was below the TRACON's MEA for that airway.

Narrative

Hand off from Approach on aircraft in the block that heads through some higher terrain deep in the approach airspace but well above our 9900 ft. Minimum IFR Altitude (MIA) well before they enter our airspace. Approach has different MIA's and so in this area this is not an unusual situation.On the pilot check in they said they were 11500 ft. Looking further out at their route I wanted to see if they would get into higher terrain past BIL or anything like that. Noticed they were on the T Route the entire way and their altitude is good for me for the T Route. But I noticed the MEA for the T-route on the portion they were on inside Approach's area is 11700 ft. I told the aircraft to climb and maintain 12000 ft. for terrain along their route; and informed Approach.I would have liked to have noticed before the aircraft checked on that it was below the MEA but I had assumed that they were clear of conflict before Approach handed them off. If the sectors weren't unnecessarily split there's a high likely hood that I would have been able to catch this issue earlier.