LESSON 10.1 & 10.2 POLYHEDRONS

OBJECTIVES:To define polyhedrons To recognize nets of space figuresTo apply Euler’s formulaTo describe cross section of 3-D figures

A POLYHEDRON

is a solid figure formed by flat surfaces enclosed by polygons.

PARTS OF A POLYHEDRON

FACES

EDGES

VERTEX

the sides (flat surfaces)of a polyhedron

the segment where two faces intersect.

the point where three or more faces intersect.

Edge Face

Vertex

Rectangular prism

How many faces does this polyhedron have? 6

Edges?

Vertices?

12

8

Euler’s Formula:

Faces + Vertices = Edges + 2

OR F + V = E + 2

Polyhedrons are classified by the number of faces.

# faces

4

5

6

7

tetrahedron

pentahedron

hexahedron

heptahedron

# faces

8

9

10

11

12

octahedron

nonahedron

decahedron

undecahedron

dodecahedron

A net is a two-dimensional pattern that can be folded to form a three-dimensional figure.

Examples Using Nets

#1 Identifying a net

Is the given pattern a net for a cube? If so, name two lettersthat will be opposite faces.

A

B F

C

D E

Yes, the pattern is a net because it can be folded to form a cube.

Opposite faces are: A C

B E

D F

and

and

and

A

B F

C

D E

#2 Draw a net for the figure with a square base and fourisosceles triangle faces. Labelthe net with its dimensions.

10 cm

8 cm 8 cm

10 cm

#3 Use Euler’s Formula to find the number of vertices on a polyhedron with 8 triangular faces.

F + V = E + 2

8 + V = 12 + 2

8 + V = 14

V = 6

Calculate edges first. 8 faces * 3 sides = 24

24/2 = 12 edges

(we do not want duplicate edges)

A cross section is the intersection of a solid and a

plane.

You can think of a cross section as a very thin slice of the solid.

Lesson 10.2

What is the shape of each cross section?

a. rectangle b. square c. triangle

d. circle e. square f. triangle

ASSIGNMENT

Pg. 514 #1-9, 13-18, 20-21, 29a AND

Pg. 524 #17-19, 40-42