JAMB 1989 · UME · Q45

$OXYZW$ is a pyramid with a square base such that $OX = OY = OZ = OW = 5$ cm and $XY = XW = YZ = WZ = 6$ cm. Find the height $OT$ .

Worked solution (try it first)

$T$ is the centre of the square base.
The base diagonal is $6\sqrt2$ cm, so $XT$ is half of it, $3\sqrt2$ cm.
In the right-angled triangle $OTX$ , Pythagoras gives $OT^2 = OX^2 - XT^2$ , which is $25 - 18 = 7$ .
So $OT = \sqrt7$ cm, option D.