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Percentage of polygon in one shapefile within polygon of another

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I’m a newbie, apologies if this is obvious/has already been asked and answered but I couldn’t find anything.

I have two shapefiles: 1. an administrative boundary layer for a county in the UK known as an LSOA boundary that has 500 little zones in it 2. a flood zone.

Ideally I want to find out which of the little LSOA zones are ≥50% within the flood zone and end up with a yes/no or a 1/0 for each of the 500 LSOA zones.

But I don’t know how to do this. I figured I could Join the two shapefiles, but there’s no common attribute between them. Then I thought I could use the Join Attribute by Location function, which worked and shows me which LSOA are in the flood zone, but that’s nearly all of them (see image 2).

I think this is an SQL problem but I don’t know. I’m new to QGIS and have never used PostgreSQL.

Any help would be greatly appreciated. I can provide whatever info you lovely people need to help me out.

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