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Mrs. Kelly Freshman 2011-2012 12.1 Three-Dimensional Figures 1-30 12.2 Nets And Surface Area 31-32 12.3 Surface Area Of Prisms 33-39 12.4 Surface Areas Of Cylinders 40-44 12.5 Surface Areas Of Pyramids 45-49 12.6 Surface Areas Of Cones 50-53 12.7 Surface Areas Of Spheres 54-57

### Isometric Grid Paper

Paper with dots equally spaced from each other forming various equilateral triangles together.

### Prism

A polyhedron with two congruent bases and with parallelogram faces. Named by the shape of the bases

### 2#

Formula for number of vertices in a prism when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### 3#

Formula for number of edges in a prism when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### # + 2

Formula for number of faces in a prism when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### Pyramid

A polyhedron with all of its faces intersecting at 1 vertex except for one. Named after their bases.

### # + 1

Formula for number of vertices in a pyramid when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### # + 1

Formula for number of faces in a pyramid when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### 2#

Formula for number of edges in a pyramid when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### Regular Polyhedron (Platonic Solid)

A polyhedron with regular, congruent polygons and congruent edges. Only 5 types.

### Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron

Group of the only 5 regular polyhedron. Name the group and each one by number of faces.

### f + v = e + 2

Euler's Theorem

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### 0.5sf

Formula for finding the number of edges in any platonic solid when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### fs/m

Formula for finding the number of vertices in a platonic solid when

f = number of faces in a polyhedron

v = number of vertices in a polyhedron

e = number of edges in a polyhedron

s = number of face sides

# = number of base sides

m = faces meeting at a vertice

### Right Prism

A prism with lateral edges that are also altitudes and therefore perpendicular to the edges

### 2B + pe

Surface area of prisms/cylinder formula when

B = area of base

p = perimeter around prism/cylinder

e = lateral edge

### Regular Pyramid

A pyramid with a regular polygon as its base and a segment connecting the center of the base to the vertex is perpendicular to the base.

### Slant Height

The height of one of the faces of a pyramid or the length from a cone's base to the vertex. Represented by a cursive l.

### 0.5pl + B

Formula for the surface area for a regular pyramid when

p = perimeter of the base

l = slant height

B = area of the base