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This question already has an answer here:

How can I calculate 3D surface area base on slope in GIS for each morphological units in watershed?

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marked as duplicate by PolyGeo♦ arcgis-desktop Sep 18 at 9:21

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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You will need 3D analyst

Create a TIN using your polygon

  • Add Surface Information with your polygon as input feature class and the corresponding TIN as input surface.
    • Check "SURFACE_AREA" box as output property.

The 3D area is then added in a new field to your polygon feature class' attribute table.

This post provides the steps Calculating 3d polygons' surface area using ArcGIS for Desktop?

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