Etymology
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Words related to *plak-

*pele- (2)
*pelə-, Proto-Indo-European root meaning "flat; to spread."

It forms all or part of: airplane; dysplasia; ectoplasm; effleurage; esplanade; explain; explanation; feldspar; field; flaneur; floor; llano; palm (n.1) "flat of the hand;" palm (n.2) "tropical tree;" palmy; piano; pianoforte; plain; plan; planar; Planaria; plane (n.1) "flat surface;" plane (n.3) "tool for smoothing surfaces;" plane (v.2) "soar, glide on motionless wings;" planet; plani-; planisphere; plano-; -plasia; plasma; plasmid; plasm; -plasm; -plast; plaster; plastic; plastid; -plasty; Polack; Poland; Pole; polka; protoplasm; veldt.

It is the hypothetical source of/evidence for its existence is provided by: Greek plassein "to mold," plasma "something molded or created;" Latin planus "flat, level, even, plain, clear;" Lithuanian plonas "thin;" Celtic *lanon "plain;" Old Church Slavonic polje "flat land, field," Russian polyi "open;" Old English feld, Middle Dutch veld "field."
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flag (n.2)

"flat stone for paving," c. 1600, ultimately from Old Norse flaga "stone slab," from Proto-Germanic *flago- (from extended form of PIE root *plak- (1) "to be flat"). Earlier in English as "piece cut from turf or sod" (mid-15c.), from Old Norse flag "spot where a piece of turf has been cut out," from flaga.

flagstone (n.)
"any rock which splits easily into flags," 1730, from flag (n.2) "flat, split stone" + stone (n.).
flake (n.)

"thin flat piece of snow; a particle," early 14c., also flauke, flagge, which is of uncertain origin, possibly from Old English *flacca "flakes of snow," or from cognate Old Norse flak "flat piece," from Proto-Germanic *flakaz (source also of Middle Dutch vlac, Dutch vlak "flat, level," Middle High German vlach, German Flocke "flake"); from PIE root *plak- (1) "to be flat." From late 14c. as "a speck, a spot."

flaw (n.)
early 14c., "a flake" (of snow), also in Middle English "a spark of fire; a splinter," from Old Norse flaga "stone slab, layer of stone" (see flag (n.2)), perhaps used here in an extended sense. Old English had floh stanes, but the Middle English form suggests a Scandinavian origin. "The close resemblance in sense between flaw and flake is noteworthy" [OED]. Sense of "defect, fault" first recorded 1580s, first of character, later (c. 1600) of material things; probably via notion of a "fragment" broken off.
floe (n.)

1817, first used by Arctic explorers, probably from Norwegian flo "layer, slab," from Old Norse flo, from Proto-Germanic *floho-, from PIE root *plak- (1) "to be flat." Related to first element in flagstone. Earlier explorers used flake. Floe-rat was a seal-hunter's name for the ringed seal (1862).

fluke (n.3)

"flatfish," Old English floc "flatfish," related to Old Norse floke "flatfish," flak "disk, floe," from Proto-Germanic *flok-, from PIE root *plak- (1) "to be flat." The parasite worm (1660s) so called from resemblance of shape.

placenta (n.)

1670s of plants, "part of the ovary of flowering plants which bears the ovules," 1690s of mammals, "organ of attachment of a vertebrate embryo or fetus to the wall of the uterus or womb of the female," from Modern Latin placenta uterina "uterine cake" (so called 16c. by Italian anatomist Realdo Colombo), from Latin placenta "a cake, flat cake," from Greek plakoenta, accusative of plakoeis "flat," from plax "flat, flat land, surface, plate," from PIE root *plak- (1) "to be flat." So called from the shape.

plagal (adj.)

denoting a mode or melody in Gregorian music in which the final is in the middle of the compass instead of at the bottom, 1590s, from Medieval Latin plagalis, from plaga "the plagal mode," probably from plagius, from Medieval Greek plagios "plagal," in classical Greek "oblique," from plagos "side" (from PIE root *plak- (1) "to be flat").

plagiarism (n.)

"the purloining or wrongful appropriation of another's ideas, writing, artistic designs, etc., and giving them forth as one's own," 1620s, from -ism + plagiary (n.) "plagiarist, literary thief" (c. 1600), from Latin plagiarius "kidnapper, seducer, plunderer, one who kidnaps the child or slave of another," used by Martial in the sense of "literary thief," from plagiare "to kidnap," plagium "kidnapping," from plaga "snare, hunting net" (also "open expanse, territory"), which is perhaps from PIE *plag- (on notion of "something extended"), variant form of root *plak- (1) "to be flat." De Vaan tentatively compares Greek plagia "sides, flanks," Old High German flah "flat," Old Saxon flaka "sole of the foot."