那个地区严重缺水,村民们挖了许多井来解决饮水问题.(LACK)

不知道你说的地区多大？大的(例如中东，南美等)用Area,较小的局部地区（东北，江淮，岭南等）用region．

That region is seriously lack of water, so the village residents there have dug many wells to solve hydrodipsia problems.