Here is an image of a triangle showing how it changes with each step. AAA a. Complete this table showing the number of shaded triangles in each step and the area of each triangle. The large outside triangle has an area of 256 in?. step number number of shaded triangles area of each shaded triangle, in 1 3 64 2 3. 4 b. Graph the number of shaded triangles as a function of the step number, then separately graph the area of each triangle as a function of the step number.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 44E
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Here is an image of a triangle showing how it changes with each step.
a. Complete this table showing the number of shaded triangles in each step and the area
of each triangle. The large outside triangle has an area of 256 in".
step number
number of shaded triangles
area of each shaded triangle, in
1
3
64
2
3
4
5
b. Graph the number of shaded triangles as a function of the step number, then
separately graph the area of each triangle as a function of the step number.
6.
Transcribed Image Text:Here is an image of a triangle showing how it changes with each step. a. Complete this table showing the number of shaded triangles in each step and the area of each triangle. The large outside triangle has an area of 256 in". step number number of shaded triangles area of each shaded triangle, in 1 3 64 2 3 4 5 b. Graph the number of shaded triangles as a function of the step number, then separately graph the area of each triangle as a function of the step number. 6.
Expert Solution
Step 1: basic information

With every 1 step, each of the given shaded equilateral triangle get divided into4 smaller equilateral triangles. All of these smaller equilateral triangles are of equal areas. Important conclusions:1.The number of shaded triangles formed from the given bigger shaded triangle, is 3.2.The area of each such triangle is 14th of the given bigger shaded triangle.    

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