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The following sequence of shapes composed of squares produces a shape called a Box Fractal if continued indefinitely. Each square is subdivided into 9 sub-squares, and the center sub-square along each side is removed. Notice how a portion of the shape at one stage is similar to a portion of the shape at another stage. Stage 1 Stage 2 Stage 3 Stage 1 Suppose the big square in Stage 1 has sides of length 9. Find the total perimeter and area of the shaded figure in each stage. Then determine what the perimeter and area of the next figure (Stage 4) would be. Stage 2 Stage 3 Stage 4 (not shown) H Perimeter H Area

The following sequence of shapes composed of squares produces a shape called a Box Fractal if continued indefinitely. Each square is subdivided into 9 sub-squares, and the center sub-square along each side is removed. Notice how a portion of the shape at one stage is similar to a portion of the shape at another stage. Stage 1 Stage 2 Stage 3 Stage 1 Suppose the big square in Stage 1 has sides of length 9. Find the total perimeter and area of the shaded figure in each stage. Then determine what the perimeter and area of the next figure (Stage 4) would be. Stage 2 Stage 3 Stage 4 (not shown) H Perimeter H Area

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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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The following sequence of shapes composed of squares produces a shape called a Box Fractal if continued indefinitely. Each square is subdivided into 9 sub-squares, and the center sub-square along each side is removed. Notice how a portion of the shape at one stage is similar to a portion of the shape at another stage. Stage 1 Stage 2 Stage 3 Stage 1 Suppose the big square in Stage 1 has sides of length 9. Find the total perimeter and area of the shaded figure in each stage. Then determine what the perimeter and area of the next figure (Stage 4) would be. Stage 2 Stage 3 Stage 4 (not shown) H Perimeter = Area Notice that the perimeter keeps increasing, but the area keeps decreasing. This is unusual.
Transcribed Image Text:The following sequence of shapes composed of squares produces a shape called a Box Fractal if continued indefinitely. Each square is subdivided into 9 sub-squares, and the center sub-square along each side is removed. Notice how a portion of the shape at one stage is similar to a portion of the shape at another stage. Stage 1 Stage 2 Stage 3 Stage 1 Suppose the big square in Stage 1 has sides of length 9. Find the total perimeter and area of the shaded figure in each stage. Then determine what the perimeter and area of the next figure (Stage 4) would be. Stage 2 Stage 3 Stage 4 (not shown) H Perimeter = Area Notice that the perimeter keeps increasing, but the area keeps decreasing. This is unusual.
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