There are multiple synonyms for the term "area unit" depending on the system of measurement being used. In the metric system, the most common unit is square meters (m^2). However, other metric units such as square centimeters (cm^2) and square kilometers (km^2) can also be used. In the imperial system, popular units include square feet (ft^2), square inches (in^2), and acres. Both systems also have their own unique units, such as "tatami" in Japanese traditional architecture, which is equivalent to approximately 1.62 square meters. It is important to note the correct unit of measurement when expressing area, as using the wrong unit can lead to incorrect calculations and confusion.