Yes, area is a derived quantity.
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Length is fundamental, area is derived.
velocity work force acceleration
Current is a basic quantity, measured in amperes.
The derived quantity is a quantity which has been derived from 2 or more base quantities. Example: Velocity is the rate of change of distance and is written in terms of distance divided by time which are two base quantities.
Derived quantities are quantities which are made or found from other major quantities. There are two types of quantities. Ones are which are recognized throughout the world and using them other quantities are made.