Prove that Euclidean area is in square units

[kotreny]

Where is it proven that the unit of area in Euclidean geometry must be a square with side=1? Or is it an axiom? Why not triangles or circles to represent area?

 

[hamster143]

That's the way it is defined. We use a square because it's most convenient.

 

[HallsofIvy]

Just seconding hamster143- the unit of area is defined as the area of a square one unit length on a side. Then we prove the formulas for areas of other figures in terms of that.