While Karl's remedy would certainly work, may I suggest that when completed, the area patched often has a different texture than the surrounding dry wall due to the filler material and the appearance doesn't diminish when painted. What I've done on several occasions is cut out the damaged area to a specific dimension, say 1/2 inch beyond the actual damage, in a rectangular or square pattern. Then cut the "patch" of dry wall material (what you call plasterboard) to almost the exact same size; glue a scrap piece of wood to the back that extends at least a couple of inches beyond the edge of the patch. After this sets up, apply glue to the ends of the wood (where it will contact the back of the patched plasterboard) and hold for a few minutes until the glue sets. You can also apply glue (sparingly) around the edges of the patch where it contacts the edges of the dry wall being patched. Once this is accomplished, if the original wall had texture applied (we'd call it orange peel), you can reproduce the texture from a spray can of obtainable at home repair store and the painted, finished area will not be noticeable. I hope this has given you a clear word picture of my intent. At any rate... Good luck!