Lesson 11-1 Pages 556-561

Three-Dimensional Figures

What you will learn!

1. How to identify three-dimensional figures.

2. How to identify diagonal and skew lines.

PlanePlane FaceFaceSolidSolid PrismPrismPolyhedronPolyhedron BaseBaseEdgeEdge PyramidPyramidVertexVertex Skew linesSkew lines

What you really need to know!

A prism is a polyhedron with two parallel bases.

A pyramid is a polyhedron with one base.

What you really need to know!

Prisms and pyramids are named by the shape of their bases, such as triangular or rectangular.

What you really need to know!

Skew lines are lines that lie in different planes and do not intersect.

What you really need to know!

A diagonal of a figure joins two vertices that have no faces in common.

Formulas for Chapter 11:

Volume of a Prism: V = Bh ; where B is the area of the Base

Volume of a Cylinder: V = Bh or V = r2h ; where B = r2

Volume of a Pyramid: V = 1/3(Bh) ; where B is the area of the Base

Volume of a Cone: V = 1/3(Bh) or V = 1/3(r2h) ; where B = r2

Surface Area of Rectangular Prisms: S = 2lw + 2lh + 2wh

Surface Area of a Pyramid: S = Area of lateral faces + Area of Base

Surface Area of Cylinders: S = 2r2 + 2rh

Surface Area of Cones: S = rl + r2

Example 1:

Identify the solid. Name the bases, faces, edges, and vertices.

G H

K J

P N

L M

This is the figure when it is unfolded!

Name: Rectangular Prism

Bases: LMNP, GHJK, KJNP, GHML, GKPL, HJNM

Faces: LMNP, GHJK, KJNP, GHML, GKPL, HJNM

Edges: GH, HJ, JK, GK, HM, MN, JN, NP, KP, LP, GL, LM

Vertices: G, H, J, K, L, M, N, P

Example 2:

Identify the solid. Name the bases, faces, edges, and vertices.

G

D F

E

Name: Triangular Pyramid

Base: DEF, EFG, DFG, DEG

Faces: DEF, EFG, DFG, DEG

Edges: DE, DF, DG, EF, EG, FG

Vertices: D, E, F, G

Example 3:

Identify a diagonal and name all segments that are skew to it.

QWQW

UVUV

UXUX

RSRS

STST

TXTX

RVRV

Example 4:

Find the area of the ground floor if each unit on the drawing represents 55 feet.

A = 5 units x 6 units

A = 5(55ft) x 6(55ft)

A = 90,750 ft2

Example 5:

How many floors are in the office building if each floor is 12 feet high? Assume each unit on the drawing represents 40 feet.

3 x 40 = 120 feet high

120 ÷ 12 = 10 floors

Page 559

Guided Practice

#’s 3-8

Pages 556-558 with someone at home and

study examples!

Read:

Homework: Pages 559-561

#’s 9-17, 22-25, 28-29

#’s 30, 31, 35-44

Lesson Check 11-1

Page

750

Lesson 11-1