# Chapter 12 Surface Area

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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

### Orthogonal Drawing

The 2-dimensional views of the top, left, front and right sides of an object

### Corner View (Perspective View)

The view of a figure from a corner. Top of 3-d figure is darkened

### Isometric Grid Paper

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

### Polyhedron

A solid with all flat surfaces that enclose a single region of space

### Face

Flat side of a polyhedron

### Edge

Line segment were the faces of a polyhedron meet

### Prism

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

### Base

One of two faces of a polyhedron, which are congruent and parallel

### Regular Prism

A prism with bases that are regular polygons

### 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.

### Triangle 4 4 6

Tetrahedron: __-shaped faces __faces __vertices __edges

Hexahedron: __-shaped faces __faces __vertices __edges

### Triangle 8 6 12

Octahedron: __-shaped faces __faces __vertices __edges

### Pentagon 12 20 30

Dodecahedron: __-shaped faces __faces __vertices, __edges

### Triangle 20 12 30

Icosahedron: __-shaped faces __faces, __vertices, __edges

### 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

### Cylinder

A circular prism (not a polyhedron)

### Cone

A circular pyramid (not a polyhedron)

### Sphere

The locus (set) of all points in space from a center.

### Cross Section

The intersection of a plane and solid when the plane is parallel to the base(s).

### Net

2-dimensional figure made when a solid is cut at the edges and laid flat

### Surface Area

The sum of the areas of each face of the solid

### Lateral Face

Face that is not the base

### Lateral Edge

Edge not part of the base

### Right Prism

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

### Oblique Prism

Prism with lateral edges not perpendicular to the bases

### Lateral Area

The sum of the areas of the lateral faces.

### pe

Formula for the lateral area of a prism when
p = perimeter around prism
e = lateral edge

### 2B + pe

Surface area of prisms/cylinder formula when
B = area of base
p = perimeter around prism/cylinder
e = lateral edge

### Axis (Of A Cylinder)

Segment with endpoints as centers of a cylinder's bases

### Right Cylinder

Cylinder with axis as an altitude and therefore perpendicular to the bases.

### Oblique Cylinder

Cylinder with axis not an altitude and therefore not perpendicular to the bases.

### 2πrh

Lateral area of a right cylinder

### 2πr^2 + 2πrh

Formula for the surface area of right cylinders when
h = height

### Axis (of a pyramid)

Segments connecting the vertex and center of the base of a pyramid.

### 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

Lateral area of a regular pyramid when
l = slant height
p = perimeter of the base

### 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

### Frustum

The part of the solid that remains after it has been cut by a plane parallel to the base.

### Right Cone

A cone with an altitude as an axis

### Oblique Cone

Cone with axis not perpendicular to the base

### πrl

Formula for the lateral area of a cone when

### πrl + πr^2

Formula for the surface area for a right cone when
l = slant height

### Great Circle

Biggest circle in a sphere, sharing a center with the sphere.

### Hemisphere

Half of a sphere and the great circle that divides it.

### 4πr^2

Formula for the area of a sphere when
r = radius of the sphere

Example: