This is the 4816th most frequent Japanese word.
泰
"泰" means "peaceful," "calm," or "great."
泰然（たいぜん） here means 'calm' or 'composed', describing someone's demeanor or state of mind as tranquil and steady.
彼は精神的にとても泰然としている。
He is mentally very composed.
泰山（たいざん） refers to Mount Tai, a symbol of stability and permanency in Chinese and Japanese culture, used metaphorically here.
この地は泰山のように安定していると聞きます。
I've heard that this land is as stable as Mount Tai.
泰平（たいへい） means 'peace' or 'tranquility,' used here to denote an era or condition characterized by peace and contentment.