Run several stages of the Sierpinski's Triangle and answer the following questions:

Write down for each Stage:

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?