Determining area of county land mass without water features using ArcGIS Desktop?

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Here are the layers that I have:

• State / Province polygon file (With Area Field)
• County / Ward polygon (with no area field), but all the polygons are within the state boundaries
• Water ways for the whole province / state. (includes rivers, lakes, creeks, brooks, etc) with no area fields

Here is what I want to do:

• Determine the gross land area of counties without the rivers and lakes.

Notes:

• The area doesn't have to be extremely precise (nearest 5 sq km is fine with me)
• Has to work on ArcMap

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