Surface Area: Add the area of every side

= ( ½ 10 12) + 2( ½ 18 8) + ( ½ 9 8) = (60) + 2(72) + (36) = = 240 u 2 12 SA = ( ) 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? units 2

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 = ( ) 20 = (15 15) + 4( ½ 20 15) = (225) + 4( 150) = = 825 u 2

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 lateral faces The shape of the base gives the figure it’s name Rectangular Pyramid Hexagonal Pyramid

12’ 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 lateral faces height

= 2(4 8) + 2(4 20) + 2(20 8) = 2(32) + 2(80) + 2(160) = = 544 u TSA = ( )(()) V= 20 = (32)(20) = 640 u = (8  4)(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 cm cm 15 in 13 in 12 in 5 in V= 12 = (52)(12) = 624 cm 3 V= = (½ 12 5) (15) = (30)(15) = 450 in 3

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 NO YES NO The face has a curve, which is not a polygon. 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 faces 11 faces 12 faces 20 faces tetrahedron pentahedron hexahedron heptahedron octahedron nonahedron decahedron undecahedron dodecahedron icosahedron 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

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 Euler 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?