Probably from a Proto-Lolo-Burmese *pra(w)ŋ ~ *prəwŋ (“to prepare, put in order, correct, change”) (STEDT root #5884; lexical entries such as "praŋ 'prepare, put in order, correct'" aren't linked to the root page for some reason), which appears to be an areal word; compare Old Chinese 備 (OC *brɯɡs, “to prepare”), and see there for more cognates.
ပြင် • (prang)
The "outside" sense appears to be perhaps derived from Proto-Sino-Tibetan *phi-r/n/s (“late, behind, after, outside”) (STEDT root #5883; lexical entries such as "praŋ 'outside'" aren't linked to the root page). Cognates could include Proto-Naga *pʰaːy (“after”), as well as Old Chinese 比 (OC *piʔ, *pis, *bi, *bis, *biɡ, “to compare, match, join, follow”) and 頻 (OC *bin, “several in succession”).
The "flat surface, shape" sense isn't given etymology by STEDT (ə-praŋ "surface, outside of a thing"). While MED apparently considers the "surface" sense separate from the "outside" sense, Luce,[1] as well as the derived terms listed by MED, seem to imply an etymological connection between the two senses, perhaps with semantic development "outside" > "broad outdoors area" > "great flat expanse" > "surface" > "shape".
ပြင် • (prang)