The acre is a unit of area and is used in the imperial and US customary systems with the symbol a.
It represents the area the size of one chain by one furlong (66 by 660 feet). This is exactly equal to 10 square chains, 1⁄640 of a square mile or 43,560 square feet.
It is generally used to measure the size of land.
The barn is a unit of area and is used in particle physics with the symbol b.
It represents approximately the area of the cross-section of a uraneum nucleus, so is very small compared to most other recognised units of area.
It is also used to measure the interaction of a nucleus with an electric field gradient in nuclear quadrupole and magnetic resonance.