Title: Lesson 1-6
Author: Tim Heppner
Last saved by: MHE
Company: MCGRAW-HILL

Geometry	Chapter 1

Lesson 1-7

Example 1  Identify Solids
Identify each solid. Name the bases, faces, edges, and vertices. 
a.		The bases are hexagons. So this is a hexagonal prism.
Bases: hexagon ABCDEF; hexagon UVWXYZ
Faces: AUVB, BVWC, CWXD, EYXD, FZYE, AUZF 
Edges: , , , , , , , , , , 
	, , , , , , , 
Vertices: A, B, C, D, E, F, U, V, W, X, Y, Z

b.	The base is a pentagon, and the five faces meet in a point.
So this solid is a pentagonal pyramid.
Base: pentagon MPRST
Faces: △OSR, △ORP, △OPM, △OMT, △OTS
Edges: , , , , , , , , , 
Vertices: O, M, P, R, S, T

c.	This solid has two circles as bases and no vertex.
So it is a cylinder.
Bases: A, Z
Faces: none
Edges: none
Vertex: none

Example 2  Surface Area and Volume

7 cm

10 cm

6 cm

8cm

a.  Find the surface area of the triangular prism.

T = Ph + 2B	Surface area of a prism 
T = (24)(7) + 2(24)	P=24, h=7, B=24 
T = 216	Simplify. 

The surface area of the prism is 216 cm².

b.  Find the volume of the triangular prism.

V = Bh	Volume of a prism 
T = (24)(7)	B=24, h=7 
T = 168	Simplify. 

The volume of the prism is 168 cm².
Example 3  Volume
POOLS   The pool at the community center is in the shape of a rectangular prism with a length of 75 feet, a width of 32 feet, and a depth of 5 feet.

a.  The manager, Ms. Thompson, needs to know the surface area of the pool before she has it repainted.  Find the surface area of the pool.

The surface area of the pool consists of the four sides and one base.

A= Ph + B	Area of the four sides + area of the base 
A = (214)(5) + 2400	P=214, h=5, B=2400 
A = 3470	Simplify.

The surface area of the pool is 3470 ft².

b.  If Ms. Thompson fills the pool to a depth of only feet, what is the volume of the water in cubic feet?

V= Bh	Volume of a prism 
V = (2400)(4.5)	B=2400, h=4.5 
V = 10,800	Simplify.

The volume of the water in the pool is 10,800 ft³.