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okay, if I have a square, and know the square footage-how can I find the middle of that square? I can't figure this out for the life of me.

  • geometry -

    If you know the area, take the √ of that area to get the length of the sides,
    e.g. area = 500 cm^2
    side = √500 = 22.36

    now you want the length of the diagonal, which is the hypotenuse.
    h^2 = side^2 + side^2
    h^2 = 2(side^2)

    h^2 = 22.36^2 + 22.36^2 = 1000
    h = √1000 = 31.6227

    The middle of that square is 1/2 way down the hypotenuse or the diagonal, which would be 15.8 for my example.

    The above is the explanation, here is the shortcut :

    double your area
    take square root of that
    take 1/2 of that answer

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