Loading in 5 sec....

How many vertices, edges, and faces of the polyhedron are there? List them.PowerPoint Presentation

How many vertices, edges, and faces of the polyhedron are there? List them.

Download Presentation

How many vertices, edges, and faces of the polyhedron are there? List them.

Loading in 2 Seconds...

- 80 Views
- Uploaded on
- Presentation posted in: General

How many vertices, edges, and faces of the polyhedron are there? List them.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

There are 10 vertices:

A, B, C, D, E, F, G, H, I, and J.

There are 15 edges:

AF, BG, CH, DI, EJ, AB, BC, CD,

DE, EA, FG, GH, HI, IJ, and JF.

There are 7 faces:

pentagons: ABCDE and FGHIJ, and

quadrilaterals: ABGF, BCHG, CDIH, DEJI, and EAFJ

Space Figures and Cross Sections

LESSON 11-1

Additional Examples

How many vertices, edges, and faces of the

polyhedron are there? List them.

Quick Check

Space Figures and Cross Sections

LESSON 11-1

Additional Examples

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

F+V= E+ 2Euler’s Formula

6 + 8 = E+ 2Substitute the number of faces and vertices.

12 = ESimplify.

A solid with 6 faces and 8 vertices has 12 edges.

Quick Check

Draw a net.

Space Figures and Cross Sections

LESSON 11-1

Additional Examples

Use the pentagonal prism from Example 1 to verify

Euler’s Formula. Then draw a net for the figure and verify

Euler’s Formula for the two-dimensional figure.

Use the faces F = 7, vertices V = 10, and edges E = 15.

F+V= E+ 2Euler’s Formula

7 + 10 = 15 + 2 Substitute the number of faces and vertices.

Count the regions: F = 7

Count the vertices: V = 18

Count the segments: E = 24

F + V = E + 1 Euler’s Formula in two dimensions

7 + 18 = 24 + 1 Substitute.

Quick Check

Space Figures and Cross Sections

LESSON 11-1

Additional Examples

Describe this cross section.

The plane is parallel to the triangular base of the figure, so the cross section is also a triangle.

Quick Check

Space Figures and Cross Sections

LESSON 11-1

Additional Examples

Draw and describe a cross section formed by a vertical plane intersecting the top and bottom faces of a cube.

If the vertical plane is parallel to opposite faces, the cross section is a square.

Sample: If the vertical plane is not parallel to opposite faces, the cross section is a rectangle.

Quick Check