The definition of area usually include the area of a rectangle definition. Can one replace it with "the area of a square of side $a$ is $a^2$"? That is can one find the area of a rectangle in this case?

  • $\begingroup$ See my answer to a similar question. Basically, you start with the axiom that the area of a $1\times 1$ square is $1$, and use further axioms to extend the definition of area to arbitrary rectangles. $\endgroup$ – TonyK Sep 2 '14 at 14:52

I've seen something like this in a textbook. Take a square and add $2$ lines to form smaller squares in opposite corners and 2 congruent rectangles. If the length of a side of one of the inner squares is $a$ and one of the other inner square is $b$, the outer square has sides of length $a+b$. So if you take the area of the outer square, subtract the areas of the other squares, and divide by $2$, you should get the area of one of the rectangles with sides of length $a$ and $b$.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.