This root is about things that happen. The verb לְאָרֵעַ means "to occur", and the nouns name the occurrence itself: an אֵרוּעַ is the word on every event invitation and news ticker in Israel. There is a second thread too: what happens is by nature passing, so the same root gives "temporary" and "transience". One root, two faces of an event: the thing that occurs, and the fact that it does not last. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Only one verb is lexicalized: pi'el לְאָרֵעַ, "to happen". An event simply occurs, so there is no causative "make happen" or passive in everyday use; the root does its real work in the nouns below.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.