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The "correct" unit will depend on the order of magnitude of the circle that you are trying to measure.

If drawn on a page, the radius is likely to be measured in inches or centimetres. In this case, the area should be given in square inches or square centimetres. But you may want more precision and measure the radius in millimetres and then the area should be in square millimetres.

A circle drawn in a field may be measured in feet, yard or metres and its area would then be in square feet, sq yards or sq metres.

The radius of the effective reach of a radio beacon may be measured in miles or kilometres and the area would then be in sq miles or sq km.

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Q: What is the Correct unit in answer when finding area of a circle?
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