4.7" is the screen diagonal. The total height, including the top and bottom border is listed as 5.44". This is according to Apple. http://www.apple.com/iphone-6/specs/

This seems unlikely, as cell phones are generally rectangular and have flat screens.

EDIT: maybe you could try drawing a screen with a 5.44" height and 4.7" diagonal. Euclid will not be your friend.

I think you and the parent are confusing the display size with phone size. The phone height is >5 inches. The display is 4.7 inches diagonally. The device size diagonally will be more than device height.

1.5" of "wasted" space? That surprises me.

There's this thing called the home button...

On most android phones that thing is part of the display that contextually hides itself, and doesn't take up extra physical space

"Most"? I've not had a single Android phone where the buttons have been part of the display. A few tablets, but no phones. I'm sure there are plenty of phones that do that too, but I've somehow managed to avoid them for the 6-7 or so Android phones I've owned.

Pretty much every Android phone released in the last 2 years besides those made by Samsung (which is admittedly a large percentage) have had on screen keys.

I've had three Android phones of different brands released in the last two years, and none of them had on screen keys. Nor did any of the other ones I considered.