Polygon assessment
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Transcript of Polygon assessment
![Page 1: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/1.jpg)
WHY some shapes TESSELLATE while
others do not?
![Page 2: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/2.jpg)
TESSELLATION[Regular]
![Page 3: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/3.jpg)
Polygon Sides Angle Sum Interior AngleTriangle 3 180 60
Triangle
![Page 4: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/4.jpg)
Does it tessellate?
![Page 5: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/5.jpg)
But….. WHY?
![Page 6: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/6.jpg)
![Page 7: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/7.jpg)
How about the other polygons?
![Page 8: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/8.jpg)
Polygon Sides Angle Sum Interior Angle
Quadrilateral 4 360 90
Pentagon 5 540 108
Hexagon 6 720 120
Octagon 8 1080 135
![Page 9: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/9.jpg)
![Page 10: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/10.jpg)
![Page 11: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/11.jpg)
HOWEVER…!
![Page 12: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/12.jpg)
Polygon Interior Angle
Pentagon 108
108+108+108 = 324108+108+108+108 = 432
The interior angles do not add up to 360o, therefore it means that regular pentagons do not tessellate.
Polygon Interior Angle
Octagon 135
135+135 = 270135+135+135 = 405
The interior angles do not add up to 360o, therefore it means that regular octagons do not tessellate.
![Page 13: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/13.jpg)
They DON’T tessellate
![Page 14: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/14.jpg)
THEREFORE,Tessellation must tile a floor with no overlapping or gaps, and they should be regular polygons.
To tessellate using the regular polygons, you need to use the ones that their interior angles add up to 360 degrees.
For triangles: interior angle = 60 degrees60+60+60+60+60+60 = 360
For squares: interior angle = 90 degrees90+90+90+90 = 360
For hexagons: interior angle = 120 degrees120+120+120 = 360
For pentagons: interior angle = 108 degrees108+108+108 = 324
![Page 15: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/15.jpg)
More Examples!!![semi-regular]
![Page 16: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/16.jpg)
6-3-6-3 TESSELLATION
![Page 17: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/17.jpg)
Triangle’s interior angle: 60o
Hexagon’s interior angle: 120o
60o+120o+60o+120o
= 180o+180o = 360o
![Page 18: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/18.jpg)
8-8-4 Tessellation
&Interior
angle of an octagon:
135O
Interior angle of a
square: 90O
135o+90o+135o
= 360o
![Page 19: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/19.jpg)
12-4-6 Tessellation
Interior angle of a
square: 90O
Interior angle of a hexagon:
120O
Interior angle of a
dodecagon: 150O
150o+120o+90o
= 270o+90o
= 360o
![Page 20: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/20.jpg)
CONCLUSION
![Page 21: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/21.jpg)
If you want to tessellate regular shapes, you need to
use the ones that their interior angles add up to
360 degrees.
![Page 22: Polygon assessment](https://reader031.fdocuments.us/reader031/viewer/2022032219/55b19edebb61ebfa2e8b457a/html5/thumbnails/22.jpg)
By ELLY LEE