Lesson 3 - Page 4


LESSON 3.  Euler’s Formula for Polygons (Lab)

MATERIALSPolyConstructo shapes, Angle ruler

PROCEDURE:  Make the given shape and then record the number of faces, the number of points (vertex), and the total measure of face angles in the data chart below.  M = the total measure of all the face angles; v = the number of vertex points 

To find the face angles, use the angle ruler.  Remember a square face would have 4 ninety degree angles for a total of 360.  A cube has 6 faces, so there would be a total of 6 x 360 for “Total measure of face angles.”

 Name Shapes needed # of faces # faces at vertex Total measure of face angles
Tetrahedron 4 eq. triangles
Hexahedron (cube) 6 squares
Octahedron 8 eq. triangles

 Now look at the data that you have collected can you see a pattern that might help you get the information without really measuring.  (clue: has to do with multiples of 360)
Icosahedron 20 triangles

Dodecahedron 12 pentagons

Hexagonal prism 6 squares  
2 hexagons

Cuboctahedron 8 eq. triangles
6 squares

Truncated tetrahedron 4 hexagons
4 eq. triangles

Rectangular prism 2 squares
4 rectangles

Rhombohedron 2 squares
2 rectangles
4 isosceles triangles

Prismatic Hexagonal dipyramid 12 isosceles triangles
6 rectangles

Look at the data and see if you can make a formula that would work on all polygons.  

Does this formula work for a cone or a cylinder? 

Why or why not?


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