polygon assessment
TRANSCRIPT
Polygon Sides Angle Sum Interior Angle
Quadrilateral 4 360 90
Pentagon 5 540 108
Hexagon 6 720 120
Octagon 8 1080 135
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.
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
8-8-4 Tessellation
&Interior
angle of an octagon:
135O
Interior angle of a
square: 90O
135o+90o+135o
= 360o
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
If you want to tessellate regular shapes, you need to
use the ones that their interior angles add up to
360 degrees.