"type of kite built on four parallel struts," 1898, from box (n.1) + kite (n.); so called for its shape.
Entries linking to box-kite
box n.1
"rectangular wooden container," usually with a lid, Old English box, also the name of a type of shrub, from Late Latin buxis, from Greek pyxis "boxwood," pyxion "writing table, box," made of boxwood, from pyxos "box tree," which is of uncertain origin. Beekes suggests a loan-word from Italy, as that is where the tree is native. Dutch bus, German Büchse "box; barrel of a gun," also are Latin loan-words.
The meaning "compartment at a theater" is from c. 1600 (box seat in the theatrical sense is by 1850). The meaning "pigeon-hole at a post office" is from 1832. The meaning "television" is from 1950 (earlier "gramophone player," 1924). The meaning "station of a player in baseball" is from 1881. The graphics sense of "space enclosed within borders and rules" is from 1929. The slang meaning "vulva" is attested 17c., according to "Dictionary of American Slang;" modern use seems to date from c. World War II, perhaps originally Australian, on the notion of box of tricks. Box lunch (n.) is attested from 1899. The box set "multiple-album, CD or cassette issue of the work of an artist" is attested by 1955. To think or act outside the box "contrary to convention" is attested by 1994.
kite n.
European bird of prey, inferior hawk (Milvus ictinus, but applied elsewhere to similar birds), Old English cyta, probably imitative of its cry (compare ciegan "to call," German Kauz "screech owl"). Of persons who prey on others, 1550s.
The toy kite, a light frame covered with paper or cloth, is first so-called 1660s, from its way of hovering in the air like a bird. The dismissive invitation to go fly a kite is attested by 1942, American English, probably tracing to the popular song of the same name (lyrics by Johnny Burke), sung by Bing Crosby in "The Star Maker" (1939):
Go fly a kite and tie your troubles to the tail
They'll be blown away by a merry gale,
Go fly a kite and toss your worries to the wind
And they won't come back, they'll be too chagrined.