This is a hollow root: the middle letter ו is a vowel that hides and resurfaces as the mould changes, which is why the family looks more scattered than it is. The core idea is to come to rest. Lanuach (לָנוּחַ) is to rest; menucha (מְנוּחָה) is calm and serenity; the biblical name Noach (נֹחַ, Noah) is built on this very root, the one who brings rest. Cause something to come to rest and you place it (לְהַנִּיחַ): a put-down object lies still. From there: a term (מֻנָּח) is a word set firmly in place, and a hanacha (a discount, also an assumption) is something laid down. 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.
Watch the hollow ו: it surfaces as a long vowel in lanuach (rest) but vanishes into a dagesh in the hif'il lehaniach (to place). The hif'il is causative in the literal sense, to make something rest = to set it down, and from "setting down" Hebrew also reaches "to assume" (you lay a premise down). The passive partners are not lexicalized; their meaning is carried by the nouns מֻנָּח and הֲנָחָה.
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.