This depends on what unit you are using to measure in. However, area will always be measure in (unit)^2.
I would use the metric unit is inches
Usually acres, but you can use whatever unit that suits your purposes.
Centimetres and millimetres.
Kilometers
Millimeters
You would use square metres (m2) to find the area of a door.
square kilometers
You can use any symbol that you like.
metres
square meter (m2)
To calculate the area of a unit circle you should use the equation x2+y2=1. The unit circle equal area of 1. You can find out more information on the mathisfun website for deeper explanation.