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Math Help - Square Galore

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    Square Galore

    Find the area of a rectangle in the margin. Everything that looks like a square is a square, and the smallest square has an area of 1.
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    Quote Originally Posted by aznmartinjai View Post
    Find the area of a rectangle in the margin. Everything that looks like a square is a square, and the smallest square has an area of 1.
    The smallest square has an area of 1, so it has a side of length 1.

    You have two small squares, so we have an area of 2.

    The square on top of them has a side of length 2, so has an area of 4.

    The square to the left has a side of length 3, so has an area of 9.

    And so on until we have the largest square having a side of length 8.

    So the area is:
    1 + (1 + 2^2 + 3^2 + ... + 8^2)

    = 1 + (1 + 4 + 9 + 16 + 25 + 36 + 49 + 64)

    = 205

    -Dan
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