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

Quadrilateral 6 8 12

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
r = radius
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
r = radius

πrl + πr^2

Formula for the surface area for a right cone when
r = radius
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

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