10-1 & 10-2: Space 10-1 & 10-2: Space Figures, Nets & DiagramsFigures, Nets & Diagrams

Objective:Objective: To recognize nets & to To recognize nets & to make isometric drawings of space make isometric drawings of space

figures.figures.

Polyhedron: A 3-dimensional figure whose surfaces are polygons.

Faces: the polygons making up the sides.

Edges: A segment that is formed by the intersection of two faces.

Vertex: A point where the three or more edges intersect.

6# of Faces: # of Edges: 12 # of Vertices: 8

Space Figures and Nets

A B C D

E

F

Net: A two-dimensional pattern that you can fold to form a three-dimensional figure.

Cube: A polyhedron with six faces, each of which is a square.

AD

F

#1 Identifying a Net

B D E F

C

A

Is this pattern a net for a cube? If so, name the letters that will appear on opposite faces.

YesOpposite faces:

Cube?

A and C;

B and E;

D and F

#2 Drawing a Net

GrahamCrackers20

147

• Draw a net for the graham cracker box. Label the net with its dimensions.

Graham Crackers

20

20

14

14

7 7 7

202014

Euler’s Formula:

The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula:

2 EVF

#3 Using Euler’s Formula:

Use Euler’s Formula to find the number of edges of a polyhedron with 6 faces and 8 vertices:

2 EVF286 E

214 E12 edges of #

#4 Using Euler’s Formula:

Use Euler’s Formula to find the number of vertices of a polyhedron with 20 faces and 30 Edges:

2 EVF23020 V

3220 V12 verticesof #

Cross-Sections

Cross Section: The intersection of a solid and a plane.