Lesson 11-1 Pages 556-561 Three-Dimensional Figures.

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Lesson 11-1 Pages Three-Dimensional Figures

What you will learn! 1. How to identify three- dimensional figures. 2. How to identify diagonal and skew lines.

PlaneFaceSolidPrism PolyhedronBase EdgePyramid Vertex Skew 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 =  r 2 h ; where B =  r 2 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(  r 2 h) ; where B =  r 2 Surface Area of Rectangular Prisms: S = 2 lw + 2 lh + 2 wh Surface Area of a Pyramid: S = Area of lateral faces + Area of Base Surface Area of Cylinders: S = 2  r  rh Surface Area of Cones: S =  rl +  r 2

Example 1: Identify the solid. Name the bases, faces, edges, and vertices.

GH KJ PN LM 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 DF 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.QWUV UX RS ST TX RV

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 ft 2

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 with someone at home and study examples! Read:

Homework: Pages #’s 9-17, 22-25, #’s 30, 31, Lesson Check 11-1

Page 750 Lesson 11-1