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6. Let Po be an equilateral triangle of area 10. Each side of Po is trisected into three segments of equal length, and the corners of Po are snipped off, creating a new polygon (in fact, a hexagon) P₁. What is the area of P₁? Now repeat the process to P₁ - i.e. trisect each side and snip off the corners to obtain a new polygon P₂. What is the area of P₂? Now repeat this process infinitely to create an object P. What can you say about the shape Po? What is the area of P?

6. Let Po be an equilateral triangle of area 10. Each side of Po is trisected into three segments of equal length, and the corners of Po are snipped off, creating a new polygon (in fact, a hexagon) P₁. What is the area of P₁? Now repeat the process to P₁ - i.e. trisect each side and snip off the corners to obtain a new polygon P₂. What is the area of P₂? Now repeat this process infinitely to create an object P. What can you say about the shape Po? What is the area of P?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.2: Perimeter And Area Of Polygons
Problem 55E: Each side of square RSTV has length 8. Point W lies on VR- and point Y lies on TS- in such a way to...
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6. Let Po be an equilateral triangle of area 10. Each side of Po is trisected into three segments of equal length, and the corners of Po are snipped off, creating a new polygon (in fact, a hexagon) P₁. What is the area of P₁? Now repeat the process to P₁ - i.e. trisect each side and snip off the corners to obtain a new polygon P₂. What is the area of P₂? Now repeat this process infinitely to create an object P. What can you say about the shape Po? What is the area of Po?
Transcribed Image Text:6. Let Po be an equilateral triangle of area 10. Each side of Po is trisected into three segments of equal length, and the corners of Po are snipped off, creating a new polygon (in fact, a hexagon) P₁. What is the area of P₁? Now repeat the process to P₁ - i.e. trisect each side and snip off the corners to obtain a new polygon P₂. What is the area of P₂? Now repeat this process infinitely to create an object P. What can you say about the shape Po? What is the area of Po?
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