I'm a little new using QGIS.
I know how to add random points within a geometry but how can I add multiple correctly distributed points within a polygon?
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You can use the tool called "regular points" (Vector-> Research Tools) in QGIS to make the points layer.
You'll want to use either the clip or intersect tool to get only the points that fall into your polygon.
Look at @Aaron's answer here: Generating regular sample points in a polygon