Chapter 8.10, Problem 2E

To determine

(a)

To find:

The missing entries in the given table with the help of given data.

Step	Number of Triangles	Length of the Base	Length of the Height	Area of One Triangle	Total Area of All Triangles
1	$1$
2	$3$
3
4
5
6

To determine

(b)

The factor by which the number of triangles increases.

To determine

(c)

The factor by which the length of the base decreases.

To determine

(d)

The factor by which the length of the height decreases.

To determine

(e)

The factor by which the area of each triangle decreases.

To determine

(f)

The factor by which the total area of all triangles changes and determine if the total area is increasing or decreasing.

To determine

(g)

To find:

A formula for the total area of the all triangles at step $n$.

To determine

(h)

To find:

The find area of the Sierpinski gasket and explain the work.