Surface Area: Add the area of every side

= (½ • 10 • 12) + 2(½ • 18 • 8) + (½ • 9 • 8) = (60) + 2(72) + (36)

= 60 + 144 + 36

= 240 u2

12

SA = + 2 + 10 ( )18

8

9

8

Net: 3-D figure unfolded

(Helps you see all the sides)

Surface Area: The sum of the areas of EACH of the faces of a 3-D figure.

We can set up SA problems just like we did the area subproblems!

One equation…four steps: 1. Picture Equation

2. Formulas

3. Simplify

4. Solve & Answer with correct units.

What type of units would be correct for Total Surface Area?units2

How many faces does the Rectangular Pyramid on the cover of your packet have?

1. Picture Equation

2. Formulas

3. Simplify

4. Solve & Answer with correct units.

15

TSA = + 415 ( )15

20

= (15 • 15) + 4(½ • 20 • 15)

= (225) + 4(150)

= 225 + 600

= 825 u2

PYRAMID

The lateral faces are not always the same size

Base: Polygon on the bottom

Lateral faces: Triangles that connect the base to one point at the top. (vertex)

base

base

lateral faces

The shape of the base gives the figure it’s name

Rectangular Pyramid

Hexagonal Pyramid

12’

10’

10’

A PRISM is:

Lateral faces may also be rectangles, rhombi, or squares.

2 congruent (same size and shape) parallel bases that are polygons

3) lateral faces (faces on the sides) that are parallelograms formed by connecting the corresponding vertices of the 2 bases.

base

base

lateral faces

height

= 2(4 • 8) + 2(4 • 20) + 2(20 • 8)

= 2(32) + 2(80) + 2(160)

= 64 + 160 + 320

= 544 u2

10

8TSA = 2 + 2 + 2

( )( () )4

20

4

20

8

V= • 20

= (32)(20)= 640 u3

8

4

= (84)(20)

triangular prism

hexagonal prism

pentagonal prism

rectangular, square, or parallelogram prism

triangular pyramid

octagonal prism

rectangular, square, or trapezoidal pyramid

pentagonal pyramid

pentagonal prism

hexagonal pyramid

Rectangular or parallelogram prism

triangular prism

On your paper, shade the figure that is the base for each of the following solids. Then name the solid using the name of its polygonal base and either prism or pyramid.

Area of Octagon =52 cm2

1. 2.

12 cm15 in

13 in

12 in

5 in

V= • 12

= (52)(12)= 624 cm3

V= • 1512

5

= (½ 12 • 5)(15)

= (30)(15)= 450 in3

Polyhedron: A 3-dimensional object, formed by polygonal regions, that has no holes in it.

SV-83

face: A polygonal region of the polyhedron.edge: A line segment where two faces meet.vertex: A point where 3 or more sides of faces meet.

Plural: polyhedra

Plural: vertices

faces

edges

vertices

SV-83

These are polyhedra:

These are NOT polyhedra:

SV-84 Classify the following as a polyhedron or not a polyhedron. Write YES or NO. If no, explain why not.

YES YES NO

YES

YES

NONO

NONO

The face has a curve, which is not a polygon.

It is only 2-dimensional.

It is only 2-dimensional

.

The face has a curve, which is not a polygon.

It is only 2-dimensional.

SV-84

Polyhedra are classified by the number of faces they have. Here are some of their names:

4 faces

5 faces

6 faces

7 faces

8 faces

9 faces

10 faces11 faces12 faces20 faces

tetrahedron

pentahedron

hexahedron

heptahedron

octahedron

nonahedron

decahedron

undecahedrondodecahedronicosahedron

Be familiar with these names.

SV-79

Complete your resource page by counting the total number of vertices, edges, and faces for each polyhedron.

Then, use the information you found to answer

SV-80

4 6 4

8 12

6

6 12

8

12

18

8

10

15

7

20 30 12

8

14

14

20

17

32

SV-80 Let VR = number of vertices, E = number of edges, and F = number of faces.

In 1736, the great Swiss mathematician Ledonhard Euler found a relationship among VR, E, and F.

Ledonhard Euler1707-1783

A) For each row, calculate VR + F.

B)Write an equation relating VR, F, and E.

See resource page.

VR + F = E + 2

SV-81

Is it possible to make a tetrahedron with non-equilateral faces? If not, explain why not. If so, draw a sketch. Yes it is possible. Shorten the length of any one edge. Possible examples:

SV-82

How many edges does the solid have? (Don’t forget the ones you can’t see.)

There are 9 edges.

There are 6 vertices.

How many vertices does it have?