Worksheet 112-2, Problem 2:

I was wondering if I overlooked a shortcut to finding the area of Iteration 0. The only ways I saw to get the area was by adding all the triangles individually, or I noted that each row of triangles starting from the top (1) increases by the next odd number to 17. So, I could add 1+3+5...+17 = 81.

I realize I can't use the formula for area of a triangle A=wh/2 because I'm using the small triangles as my unit.

I do understand how to get the area for Iterations 1 & 2 using the answer for Iteration 0.

Thanks,
Liam

Dear Liam,


You raised a very good question. I like how you looked for a shortcut and actually there is one, but it hasn't been included in a lesson. Notice that
1 + 3 = 4 = 2 x 2
1 + 3 + 5 = 9 = 3 x 3
1 + 3 + 5 + 7 = 16 = 4 x 4


Just think about the pattern and you will have your answer. Thanks for writing.


Joan A. Cotter, Ph.D.

I do see the pattern that you started. That's a really cool shortcut!

Thanks a lot.

Liam