'GIS: Alternative ways of patching gaps in a polygon

I'm working in QGIS but I can also use ArcGIS if there's a solution that works best on there.

I have a shapefile with certain plots of land highlighted and I plan to calculate the distance of features to the borders of these plots. But the plots have the roads and rivers going through them as gaps in the polygons. Like this:

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Of course, this messes with the distance calculation I want. The goal is to create new polygons that just the outline only. I have tried the hole function in QGIS. I also tried buffering with dissolving then reversing the buffer. What other methods might work to fill in the gaps?



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