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Continue selecting on the solid model until one of the surfaces highlights. Then use the control key to continue selecting the surfaces that you want.
Then Edit-Copy, Edit-Paste. Take the default and select green check to create the surface set.
Next: Analysis-Measure-Area. Right click over the area set just created and select "pick from list". Select the quilt in the feature set, "ok".
The area of the surfaces will display in the area box.