Projecting iPad 2 wirelessly on old projector & apple tv

Posted this in the wrong forum originally


iPad - HDMI to VGA Adapter Bluetooth for audio.
I am trying to find a possible solution for hooking an iPad up to a projector wirelessly without havig to buy a 1000+ wireless projector with HDMI

I am going to use Apple TV

Use a HDMI to VGA adapter to put it into the existing projector.

However this will not allow for the output of sound.

Could I use a Bluetooth speaker for sound output on this set up?

So my only options to hook the apple tv up to a HDMI projector?

Could I wirelessly project with a witless projector?