A Center Controller reported they issued a direct routing to a helicopter which placed it 100 ft. below the Minimum Enroute Altitude.

Narrative

I was working the midshift. Aircraft X was a medevac departed ZZZ area enroute to ZZZ1 (hospital helipad around ZZZ2). The aircraft picked up their IFR in the air requesting 3000 ft cruise altitude. I cleared the Aircraft X as filed direct ZZZ1 maintain 3;000 ft. I did not realize their route eventually put them through the small circled area that has an MEA of 3;100 ft. I only became aware after they had already entered this area that they were 100 feet low. The event occurred because I failed to consider that small area in that had an MEA at 3100 ft. But I should have checked that considering the aircraft was so low on IFR flight plan.I don't think there is any change necessary to prevent re-occurrence of this event. I'd just say that personally I should have had more awareness of the airspace and MEAs and checked if the aircraft was going to go through any areas with an MEA higher than 3;000 ft. Thankfully the aircraft was only 100 ft. low for a short time and there was no incident. However I will be extra careful to avoid this mistake in the future.