Airplay doesn't fit screen! (pictures included)

I've just installed a new 1080p projector and connected my iPad 3 to it.

 

When using Apples standard VGA Adapter the iPad fills the whole screen on the projector, see picture: https://www.dropbox.com/s/mqhpyrfv6d7omgn/VGA.JPG

 

But when im connecting an Apple TV 3 and using screen mirroring via Airplay, the picture gets smaller, see picture: https://www.dropbox.com/s/wbxfbo4cxgbp4me/ATV.JPG

 

 

I can't find any reasonable explanation to why this happens, so I'm asking here. Is there any solution?

 

Thanks!

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