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The total area can be easily calculated by creating a buffer around the vector polygon feature, converting it into a raster with a pre-determined cell size, reclassifying it into a binary layer to capture all cells within the buffer as 1 and all NoData cells as 0, then conducting map algebra with a boolean operator to overlay the reclassified raster ontop of the original vector, and then counting all the 1s in the attribute table and multiplying by the cell size, twice.