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The unit of area "one square meter" or "one square foot" is DEFINED as the area of a square with sides of length 1 meter or 1 foot. This works for any unit of distance measurement. So we start with this definition. It follows that a square with sides of length n when n is an integer has area n2 square units because it can be divided into n*n= n2 small squares one unit on a side. For the area of a square with sides of fractional length, we can use a proof that calls upon similar polygons. This proves the area exists, it does NOT prove it is unique. To prove that, assume it is not uniqe and arrive at a contradiction.

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Q: Proof to find the area of a square?
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How find the area of a square when a circle is inside?

You find the area of the whole square first. Then you find the area of the circle inside of it And then subtract the area of the circle from the area of the square and then you get the shaded area of the square


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