SLO 4.x Similar Solids and Euler's Formula

Scaling Solids and Euler's Theorem

SLO 4.x

Example 1:

• Triangular Prism

• 5 Faces

• 6 Vertices

• 9 Edges

Example 2:

• Pentagonal Pyramid

• 6 Faces

• 6 Vertices

• 10 Edges

Example 3:

• Hexagonal Prism

• 8 Faces

• 12 Vertices

• 18 Edges

Open Ended

What type of polyhedron did you and your partner construct?​ ​ ​

Open Ended

What was the scale factor you used $$k$$ ?

What was the area scale factor $$k^2$$ ?

What was the volume scale factor $$k^3$$ ?

Open Ended

How many Vertices on your polyhedron $$V$$ ?

How many Edges does your polyhedron have $$E$$ ?

How many Faces does your polyhedron have $$F$$ ?

Multiple Choice

Does the number number of Faces plus the Vertices equal the number of Edges plus 2?

$$F+V=E+2$$

• True

• False

Multiple Choice

Euler's Formula is

• F + V - E = 2

• F + E - V = 2

• F - V + E = 2

• F + V + E = 2

Multiple Choice

A polyhedron has 6 faces and 7 vertices. How many edges does it have?

• 11

• 14

• 17

• 25

Multiple Choice

A polyhedron has 25 faces and 36 edges. How many vertices does it have?

• 11

• 12

• 13

• 14

Multiple Choice

 A polyhedron has 6 vertices and 9 edges. How many faces does it have?

• 3

• 5

• 7

• 9

Multiple Select

Put a check next to the correct facts about this Hexagonal Prism:

• There are 8 Faces

• There are 6 Faces

• There are 12 Edges

• There are 18 Edges

• There are 12 Vertices