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A regular octagon is formed by cutting off the corners of a square. If one side of the square is n cm, find the total area removed in square cm.

  • Mathematics -

    If the length of the corners cut off is s, the diagonal length is s√2.

    The area of each triangle is thus 1/2 (2s^2) = s^2

    Now, we know that 2s + s√2 = n, so

    s = n/(1+√2)

    The area cut off is thus 4n^2/(3+2√2) = 4(3-√8)n^2

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