How to measure the distance between multiple points and multiple polygons?

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I'm trying to find a quick and accuarate way to measure the distance between 3 survey sites and all the designated sites within 10km. The survey sites are on a point vector layer and the designated sites are polygons, both on the same CRS.

I am new to GIS and so far I have only been able to measure the distance to the nearest designated site. As I said I need to know the distance to the nearest boundary of all the sites within 10km, not just the nearest.

All help would be greatly appreciated, but please keep it simple if possible.

Many Thanks



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