QGIS boundary select smaller polygons that are contained within larger polygon

Question

I have two layers which are perfectly nested. There are dozens of SA1 polygons (thin grey outline - see image attached) within the LGA polygon (thick green outline - see image attached). I would like to select all SA1s within the larger LGA polygon.

When I try and do this with the "select by location" tool by choosing "are within" it excludes SA1s where the centroid is clearly within the LGA boundary but may slightly intersect. When I choose "are within" and "intersect" it then spills over the LGA boundary.

The second image shows the ideal end state of what I am trying to achieve.

This is a very simple task in MapInfo using the boundary selection tool but is much harder in QGIS.

Answer 1

So if I understand correctly the way I'd get the selection you're after is by using "Intersection" on the two polygon layers while you have the one larger polygon area selected.

Starting Image

1 Step; Select the larger polygon and run Intersection, Larger polygon as input with selected futures only, overlay layer smaller polygons that overlap the larger polygon.

Final overview of the intersection; As you can see the polygons are not exceeding the outline of your larger polygons and will inherit the attributes of the previous polygons.