Run several stages of the Sierpinski's Triangle and answer the following questions: [list] [*]Write down for each Stage: [list] [*]Number of Shaded Triangles [*]Area of one Shaded Triangle [*]Total Shaded Area [/list] [*]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? [/list]