Exploring generations of similar figures. (Each must be the same shape but larger.) For example, how many square pattern tiles will you use to create the next larger square for each generation? How many triangle tiles will you use to create the first generation, second generation, third generation, and so forth?

Draw the first through the fifth generations of squares, triangles and trapezoids. Count how many of each shape are needed to create each generation.
Explain the pattern that you have observed. If a pattern does hold for each generation, how many tiles would be required at the 20th generation?
How do you determine if the generation you are building is similar (by mathematical definition) to the other generations?
What happens to area when you double the dimensions of a given polygon? Triple them? Describe the pattern and give the value needed for the 20th generation.