Earlier quoted context omitted.
But manhole covers are always bigger than the hole. Otherwise, they'd fall in at installation and the problem would be immediately obvious. The point here is more that a circle has the same diameter regardless of orientation. There's no way to rotate it to make it fit through a hole it couldn't before, like you can do with a rectangle.
This is also true of a triangle, and indeed there are triangular manholes.
The height of an equilateral triangle is about 87% of the length of one of its sides.