Height was the distance from an object's lowest point to its highest.
In 2269, after rescuing her from an aquarium, a two inch tall James T. Kirk asked an equally miniaturized Nurse Christine Chapel not to climb any more heights. Before Kirk beamed down to Terra 10, Spock questioned whether the transporter would retain his current height as well as his molecular structure. (TAS: "The Terratin Incident")
In 2369, while aiding in a holographic re-creation of a table seen by several members of USS Enterprise-D's crew, La Forge asked the computer to reduce the table's height by twenty five percent. (TNG: "Schisms")
Also that year, a malfunction in The Doctor's imaging system was reducing his height by five centimeters every hour. Kes noticed that his head, which was as tall as a cabinet in sickbay, was now ten centimeters below it. The Doctor corrected her, saying that it was 10.4 centimeters. Later, he discussed his problems as well as unusual symptoms being experienced by some of his patients, all of which Janeway believed could be attributed to a quantum singularity. (VOY: "Parallax")
In 2376, when returning officer Lyndsay Ballard asked Mezoti to patch her through to Captain Kathryn Janeway, the young Norcadian said she'd try, but that her "height may be insufficient". (VOY: "Ashes to Ashes")
Later, The Doctor requested B'Elanna Torres change the placement of chairs in an auditorium for his opera performance for the Qomar, as given the height of the average Qomar, those in the back five rows would not be able to see him as well. (VOY: "Virtuoso")
In 2377, Tuvok asked Harry Kim for a description of an unknown intruder, including height and weight. Kim estimated between 170-190 cm, and about 75 kg. Tom Paris noted that that would describe about half of USS Voyager's crew. Later, the ship's computer confirmed that Tuvok's height and that of the intruder were identical, one hundred and eighty-two centimeters. (VOY: "Repression")