1. Have Out: Bellwork: 7/11/12 Homework, red pen, pencil, gradesheet
Find the Area 2
h2 = (Pythagorean. Thm.)
15 ft
h2 = h
10 ft
h = 15 ft
P =
24 ft
= 66 ft.

2. A = + = (10  15) + ( 12  9) = 150 + 54 = 204 ft2 1 Picture Equation
Formulas
10 ft 3
Simplify 4
Solve
24 ft
A = 10 12 15 9 1
= (10  15) + ( 12  9) 2 =
= 204 ft2

3. Surface Area: Add the area of every side

4. ( ) SA = + 2 + = (½ • 10 • 12) + 2(½ • 18 • 8) + (½ • 9 • 8)
Net: 3-D figure unfolded
(Helps you see all the sides) 12
SA = 10 ( ) 18 8 9
= (½ • 10 • 12) + 2(½ • 18 • 8) + (½ • 9 • 8)
= (60) + 2(72) + (36) =
= 240 u2

5. Add to your notes...
Total Surface Area:
The sum of the areas of EACH of the faces of a polyhedron.
We can set up TSA 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

6. How many faces does the Rectangular Pyramid on the resource page have?
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How many faces does the Rectangular Pyramid on the resource page have? 5 15
TSA = ( ) 20
1. Picture Equation
= (15 • 15) + 4(½ • 20 • 15)
2. Formulas
= (225) + 4(150)
3. Simplify =
4. Solve & Answer with correct units.
= 825 u2

7. Add to your notes: PYRAMID Base: Polygon on the bottom
Rectangular Pyramid
PYRAMID
Base: Polygon on the bottom
base
The shape of the base gives the figure it’s name
lateral faces
Lateral faces: Triangles that connect the base to one point at the top. (vertex)
The lateral faces are not always the same size
base
Hexagonal Pyramid

8. 12’
10’

9. Add to your notes: A PRISM is:
base
2 congruent (same size and shape) parallel bases that are polygons
height
3) lateral faces (faces on the sides) that are parallelograms formed by connecting the corresponding vertices of the 2 bases.
base
lateral faces
Lateral faces may also be rectangles, rhombi, or squares.

11. rectangular, square, or parallelogram prism pentagonal 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.
triangular prism
rectangular, square, or parallelogram prism
pentagonal prism
hexagonal prism
triangular pyramid
octagonal prism
rectangular, square, or trapezoidal pyramid
pentagonal pyramid
Rectangular or parallelogram prism
triangular prism
pentagonal prism
hexagonal pyramid

12. ( ) V= • 20 = (84)(20) = (32)(20) = 640 u3 TSA = 2 + 2 + 210 8
TSA = ( ) 4 20
= 2(4 • 8) + 2(4 • 20) + 2(20 • 8)
= 2(32) + 2(80) + 2(160) =
= 544 u2

13. V= • 12 V= • 15 = (52)(12) = (½ 12 • 5)(15) = 624 cm3 = (30)(15)1. 2.
12 in
5 in
15 in
12 cm
13 in
Area of Octagon =52 cm2 12
V= • 12
V= • 15 5
= (52)(12)
= (½ 12 • 5)(15)
= 624 cm3
= (30)(15)
= 450 in3

14. Polyhedra Add to your notes... Polyhedron:
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Polyhedra
Add to your notes...
Polyhedron:
A 3-dimensional object, formed by polygonal regions, that has no holes in it.
Plural: polyhedra
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: vertices
faces
vertices
edges

15. These are NOT polyhedra:
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These are polyhedra:
These are NOT polyhedra:

16. SV-84
Classify the following as a polyhedron or not a polyhedron. Write YES or NO. If no, explain why not.
YES
YES NO
The face has a curve, which is not a polygon. NO
It is only 2-dimensional.
YES NO
It is only 2-dimensional.
The face has a curve, which is not a polygon.
It is only 2-dimensional. NO NO
YES

17. Be familiar with these names.
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Polyhedra are classified by the number of faces they have. Here are some of their names:
4 faces
tetrahedron
9 faces
nonahedron
5 faces
pentahedron
10 faces
decahedron
6 faces
hexahedron
11 faces
undecahedron
7 faces
heptahedron
12 faces
dodecahedron
8 faces
octahedron
20 faces
icosahedron
Be familiar with these names.

18. Then, use the information you found to answer
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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
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19. 4 6 4 8 8 12 6 14 6 12 8 14 12 18 8 20 10 15 7 17 20 30 12 32

20. A) For each row, calculate VR + F. See resource page.
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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.
A) For each row, calculate VR + F.
See resource page.
Write an equation relating VR, F, and E.
VR + F = E + 2
Ledonhard Euler

21. Yes it is possible. Shorten the length of any one edge.
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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:

22. How many vertices does it have?
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How many edges does the solid have? (Don’t forget the ones you can’t see.)
There are 9 edges.
How many vertices does it have?
There are 6 vertices.