Hey I never said you couldn't use a calculator!
Places left desolate by evil:
Ard-Galen (Anfauglith)
Dale (Desolation of Smaug)
Dagorlad*
Hollin
Field beneath the Party Tree in Hobbiton.**
*I don't know if this counts a a part of Mordor or not because its so close.
** A little small to count as a
region, but it could work...