10. The Koch Snowflake is a mathematical shape known as a fractal that has many fascinating properties. It is created by repeatedly forming equilateral triangles off of the sides of other equilateral triangles. Its first six iterations are shown to the right. The perimeters of each of the figures form a geometric sequence. (a) If the perimeter of the first snowflake (the equilateral triangle) is 3, what is the perimeter of the second snow flake? Note: the dashed lines in the second snowflake are not to be counted towards the perimeter. They are only there to show how the snowflake was constructed. (b) Given that the perimeters form a geometric sequence, what is the perimeter of the sixth snowflake? Express your answer to the nearest tenth. (c) If the this process was allowed to continue forever, explain why the perimeter would become infinitely large.

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