My son's studying Chinese. His teacher asked how 念 semantically appertains to its components 今心. I don't speak Chinese, and he had no idea. Then we resorted to Wiktionary that refers to Axel Schuessler, ABC Etymological Dictionary of Old Chinese (2007), page 400. Pls see my red underline beneath.
This answer is still incomplete!
Chinese is grouped in the Sino-Tibetan language family as determined by experts on account of certain features that are unlikely to be coincidental, pointing to a deeper genetic relation. Khmer is in a different language family, whose stemming is contested because many affiliations are less than clear. South East Asian share many features that may have diffused horizontally through language contact. This is sometimes called a Sprachbund (from German Sprache "language, speech" + Bund "bond, federation", coined in reference to the Balkans Sprachbund).
Chinese research on the other hand has the practical advantage of a written tradition, attestation beginning with Oracle Bone Script sometime before the common era, dispersing widely and culminating in the first millenium in a dictionary for a courtly branch of this tradition, that is now called Shouwen, in which the author tried to categorize and etymologize characters. These etymologies are not always correct, current research shows, as they did not have the necessary depth, and they may be better thought of as memory aid. How traditional or, in a sense, correct those folk etymologies were is not clear. Anyway, this is likely what the teacher is asking for. That's different from an etymology for the spoken word.
For the Chinese and Khmer words to be "related" or not, as one comment puts it (@jogloran), the language families have to be related, in a technical sense, for vertical transmission along the branches of a family tree to occur. Schuessler does a priori not assume any such relation. Nevertheless, it's not entirely out of the question that the languages share some words. This tends to be a difficult topic, because it needs a framework in which language contact is possible.
An area word in this sense would simply mean that the word was common in an area of language contact. Diglossia, that is bilungualism with a dominant standard language in contrast to regional vernacular to various degrees of profficiency is said to be statistically more common than not. However, it's not said where this would have occurd. It's possible that Schuessler's book has an introduction outlining his basic assumptions, detailing which ones of these need to be understood as research problems in need of further investigation, but the choice of verbiage, ie. area word, might be arbitrary at that (and I do not have the book at hand nor any investment in this field).
If there is further research to be found in the more recent literature, or if it is enough to point out an acceptible derivation for only one half of the equation to rule out horizontal transmission (as @jogloran seems to suggest, prerequisite that transmission from Proto-Mon-Khmer to Chinese was out of the question).
For the sake of completeness 💭 let's note that visual representation of an abstract concept like"to think of, remember, remind" is necessarily difficult, and that spatially and object information is prevalent in the mental space,
