How to set the sheet size in Altium Designer?
Printing is different from the (virtual) document size. The schematic document size sets the proportions and the mapping from the symbol size to document. 

The printed page dimensions and scaling are set by File->Page Setup. You probably would want to set the two the same. The default is probably 'letter' (215.9mm by 279.4mm) not 'A4' (210mm by 297mm). 





Edit: You can see the print area by right-clicking in the preview pane and selecting appropriate options. The available area changes with the selected printer. It does appear that, for whatever reason, they've chosen to make the aspect ratio a bit different from that of the paper, leaving a few mm more space top and bottom. 

Of course when you make your own template (which you would definitely want to do, to include your company logo and your custom title block) you can alter it if you want.