Figure showed up in the thirteenth century, first just meaning a number and then a century later meaning the image of a person, and also the verb form. Although again, initially the verb didn’t mean what we know it as (as in, to figure something out). It used to just to represent, then make a likeness of. It wasn’t until the seventeenth century that it meant “picture in the mind”, and then not until 1833 was it used in math. It comes from the Old French figure, which could mean shape or body, the form of a word, or a symbol. Funny how initially only one of those definitions was used in English. Anyway! Before that, it comes from the classical Latin figura, shape or figure, which is related to figurare, to shape or figure and from the Proto Indo European root dheigh-, form or build. Which is where we get the other words we’re looking at today.
Figment showed up in the early fifteenth century from the classical Latin figmentum, figment or fiction, which is also derived from figura. Also, configure showed up in the late fourteenth century as to form or “to dispose in a certain form” because words are weird. It comes from the classical Latin configurare, to configure, a mix of the prefix con- (with or together) and figurare, to shape. To configure is to shape together. Which means reconfigure is to shape together again. Similarly, transfigure is trans- (across or beyond) + figurare, to shape beyond.
There are a bunch of other words that are descended from dheigh-. Effigy is ex- (out) plus fingere, another word that also means form or shape. Feign, feint, fiction… But not significant. Which is from sign.
We’ll get into those other words another time.