A ballroom is 25 feet long by 15 feet wide, with a ceiling 15 feet from the floor -- like a matchbox with two 25 x 15 side walls and two 15 x 15 end walls.

A glitterball hangs on the far-end wall at a spot 14 feet from the floor, equidistant from both side walls.

An ant is at a startpoint on the near-end wall 14 feet from the floor, equidistant from the two side walls.

This ant will win the glitterball if it traverses any surface whatsoever travelling from startpoint to endpoint covering the shortest distance possible. What is the shortest distance?

For clarification:

1) Are we meant to assume the glitterball is the endpoint?
2) How does one hang a glitterball from a wall? Don't they usually hang from ceilings?

Yes, the glitterball is the endpoint.
The glitterball was hung on the end wall by Jodie standing on Ian's shoulders. The ceiling was just out of reach, so they settled for nailing it at 14 foot above the floor. I saw them do it.

I assume 27 feet is too obvious, but I'm not seeing why it's wrong.

(You'd normally make this more interesting by, say, having the ant start at floor level).

27 ft

Well spotted. This is a DANCE competition, so the ant must set foot on the dance floor at least once.

Unfortunately, you omitted to mention this in the original spec!!

Ah, but you didn't say that. You just said traverses any surface whatsoever travelling from startpoint to endpoint covering the shortest distance possible. And after all, if Lionel Richie can do it, why can't the ant!

*has brilliant image of Post-Office-style ant in white suit and medallion, doing groovy dance next to upside-down glitterball*

Not sure, but I'll guess the best is 4 sqrt(149) ? (Imagine 'unfolding' the two end walls and the one side wall to get a 15 x 55 rectangle. The ant heads straight for the floor at the "27.5" midpoint and then straight for the glitter ball).