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How can I prove that the area of a square is $s^2$?

I have searched the internet, but I haven't found a direct answer.

Mathew
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  • The exact flavour of proof will very much depend on how you define the term "area". What is the definition you are using? –  Dec 03 '21 at 14:31
  • We could argue that essentially the definition of "area" is "the notion of area such that the area of any square of side $s$ is $s^2$". –  Dec 03 '21 at 14:37

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Metre square, centimetre square, kilometer square. We measure are in squares Literally. A metre square is a square with sides of length 1m, a centimetre square square with sides of length 1cm and so on. And when we say a 2cm square it means we have 2 squares with square with sides of length 1cm.

So basically calculating the area a shape is counting the number of square the shape in made out of.

If we have a square with side of length a then that means we will a number row consisting of a number of square. So to count all the square we have to a, a number of times which is a X a therefore the ares of the square is a^2

Ludwig
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