Sierpinski's Triangle Exploration Questions Run several stages of the Sierpinski's Triangle Activity, and answer the following questions: Fill in the table: Iteration   1     2     3     4   Number of Shaded Triangles         Area of one Shaded Triangle         Total Shaded Area         What patterns do you see in the numbers for the number of shaded triangles? Can you build a formula for the number of shaded triangles at the n-th stage? What patterns do you see in the numbers for the area of one shaded triangle? Can you build a formula for the area of one shaded triangle at the n-th stage? What patterns do you see in the numbers for the total shaded area? Can you build a formula for the total area at the n-th stage? What do you think happens to these numbers as the number of stages approaches infinity? Compare these results to those for the Sierpinski's Carpet. Does the "three-ness" of a triangle and the "four-ness" of a square seem to play a role in these numbers?