Chapter 10 day 1 s.a. of prisms

Drill GT Geom 5/7/14

Find the unknown lengths.

1. the diagonal of a square with side length

5 cm

2. the base of a rectangle with diagonal 15

m and height 13 m

3. the height of a trapezoid with area 18 ft2

and bases 3 ft and 9 ft

OBJECTIVETo find lateral area

and surface area of a polyhedron,

the prism

Key TermsPolyhedron

Altitude

Lateral Area

Net

Three-dimensional figures, or solids, can be made up of flat

or curved surfaces. Each flat surface is called a face. An

edge is the segment that is the intersection of two faces. A

vertex is the point that is the intersection of three or more

faces.

A cube is a prism with six square faces. Other prisms and

pyramids are named for the shape of their bases.

PostulateWrite the formula for the volume of a right rectangular prism.

V = lwh We will assume prisms

are RIGHT from now on

VocabularyPolyhedron- A geometric solid with polygons as faces.

DEFINITIONPrism-A polyhedron with two polygonal bases that are parallel and congruent.

Right Prism - lateral edges are perpendicular to the planes of the bases.

VocabularyAltitude of a Prism - any segment perpendicular to the planes containing the bases with endpoints in these planes. ( same as HEIGHT)

VocabularyNet - a figure that can be

folded to enclose a particular solid figure

ClassworkDraw a net for a right triangular prism.

Draw a net for a right pentagonal prism.

Classwork

Classwork

Example 2A: Identifying a Three-Dimensional

Figure From a NetDescribe the three-dimensional figure that can be made from

the given net.

The net has six

congruent square faces.

So the net forms a cube.

Example 2B: Identifying a Three-Dimensional

Figure From a NetDescribe the three-dimensional figure that can be made from

the given net.

The net has one circular face

and one semicircular face.

These are the base and

sloping face of a cone. So the

net forms a cone.

Check It Out! Example 2a

Describe the three-dimensional figure that can be made from

the given net.The net has four

congruent triangular

faces. So the net forms a

triangular pyramid.

Check It Out! Example 2b

Describe the three-dimensional figure that can be made from

the given net.The net has two circular

faces and one rectangular

face. These are the bases and

curved surface of a cylinder.

So the net forms a cylinder.

Lateral Area of a Prism - sum of the areas of the lateral faces.

Surface Area of a Prism - sum of the lateral area and the areas of the two bases

Classwork

LATERAL AREA

SURFACE AREA

Prisms and cylinders have 2 congruent parallel bases.

A lateral face is not a base. The edges of the base are called

base edges. A lateral edge is not an edge of a base. The lateral

faces of a right prism are all rectangles. An oblique prism

has at least one nonrectangular lateral face.

Lateral Area of a Right Prism

Is their a short cut for finding the lateral area ?

Lateral Area of a Right Prism

The lateral area LA of a right prism with height h and perimeter of base p is:

LA = Hp or L = Hp

Surface Area of a Right PrismThe surface area SA of a

right prism with lateral LA and the area of a base B is:

SA = LA + 2B

or S =L + 2B

Volume

Volume equals Area of the Base times the Height of the object.

V = BHArea of the Base x Height of the object

Find the LA

Find the SA

Lateral Area of a Right Prism

Find the lateral area LA of a right prism with height 10cm, if the base is a regular hexagon with side 3cm.

Find the surface area SA of a right prism with height 10cm, if the base is a regular hexagon with side 3cm.(round answer to nearest hundredth)

Example 1: Drawing Orthographic Views of an

ObjectDraw all six orthographic views of the given object. Assume

there are no hidden cubes.

Example 1 Continued

Draw all six orthographic views of the given object. Assume

there are no hidden cubes.

Bottom

Example 1 Continued

Draw all six orthographic views of the given object. Assume

there are no hidden cubes.

Example 1 Continued

Draw all six orthographic views of the given object. Assume

there are no hidden cubes.

Check It Out! Example 1

Draw all six orthographic views of the given object. Assume

there are no hidden cubes.

Check It Out! Example 1 Continued

Classwork/HomeworkPractice and Apply 7.2P685 #’s 13-26 and 28-31

Three-dimensional figures, or solids, can be made up of flat

or curved surfaces. Each flat surface is called a face. An

edge is the segment that is the intersection of two faces. A

vertex is the point that is the intersection of three or more

faces.

A cube is a prism with six square faces. Other prisms and

pyramids are named for the shape of their bases.

Prisms and cylinders have 2 congruent parallel bases.

A lateral face is not a base. The edges of the base are called

base edges. A lateral edge is not an edge of a base. The lateral

faces of a right prism are all rectangles. An oblique prism

has at least one nonrectangular lateral face.