After years of studying math, I still have this basic question.
I learned areas of square, triangle, and others as they are by listening to what was told in elementary school. However, I then know a rectangle is just two right triangles and a right triangle is half of a rectangle. Hence, when asked by non-math people why a rectangle's area is its length times height, I usually used two right triangles, then used the summation of the known formula of triangle's area. However, it definitely works either way.
So I am pretty sure something must be asked by me about the definition of area. I just thought that I can get a triangle by cutting a parallelogram which is just a rectangle with a part sliced and moved to the other end, but I also can get a parallelogram by combining two triangles, and do a reverse step to get a rectangle. Then, which one comes first, egg or chicken?
I looked at the Wiki page and it looks like we can use an axiom which is based on rectangle. Or that we assume a square of sides 1 has area 1 and deduce everything from it by slicing, etc. However, I also think that triangle is more fundamental as only by using at least three sides/lines (Euclidean plane), we can finally has an enclosed area, whereas four sides are not necessary.
Does it work either way? Thanks for the lights. :)
EDIT: My guess is that it works either way, but, perhaps, a square is more natural/intuitive/easier, I guess? Not quite sure hahaha