Raster Area within a Polygon

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using ArcGIS, I have a layer of overlapping polygons and a raster grid underneath. The raster is not a continuous grid - the cells are spread out. I simply need to calculate the total area of the raster that falls within each feature of a polygon layer.

I've used Zonal Statistics and it works great for isolated polygons, however the polygons that overlap each other are not resulting in the correct pixel count for each individual polygon.

Thanks!





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