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Right Triangular Prism |
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Prisms
are three-dimensional closed surfaces.
A prism has two parallel faces, called
bases, that are congruent polygons. The
lateral faces are rectangles in a
right prism, or parallelograms in an oblique prism. In a
right prism, the joining edges and faces are perpendicular to
the base faces. |
Prisms are also called polyhedra
since their faces are polygons.
A regular prism
is a cube.
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Right Rectangular Prism |
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Oblique Triangular Prism |
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Parallelepiped
A prism which has a parallelogram
as its base is called a parallelepiped. It is a polyhedron with 6
faces which are all parallelograms. |
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The edges of the prism
where the lateral faces intersect are called its
lateral edges. The
lateral edges in a prism are congruent and parallel.
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Lateral edges:
There are 5 congruent and parallel lateral
edges in this prism. |
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The
volume
of a
prism is the product of the base area times the
height of the prism.
V = Bh
(Volume of a prism:
B = base area, h = height) |
h
= height(altitude) between bases
B
= area of the base |
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The
surface area of a prism is the
sum of the areas of the bases plus the areas of the lateral
faces. This simply means the sum of the areas of all
faces.
The surface area, S, of a right prism can
be found using the formula S = 2B +
ph.
B = area of base, p =
perimeter of base, h = height. |
A net is a
two-dimensional figure
that can be cut out and folded up to
make
a three-dimensional solid. |
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Note: A cross section
of a geometric solid is the intersection of a plane and the solid.
A prism has the same cross section
(parallel to the base)
all
along its length !
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Shown here are the cross sections
(in the same plane) of two prisms of equal height. The
cross section slices are indicated in red and are parallel to
the bases.
If the areas of these two cross section slices are equal, the prisms will
be equal in volume. |
Seventeenth century mathematician,
Bonaventura Cavalieri, generalized this concept for solids.
| Cavalieri's
Principle: If, in two solids
of equal height, the cross sections made by planes parallel
to and at the same distance from their respective bases are
always equal, then the volumes of the two solids are equal. |
For
Algebra 1 you should know a generalized statement of this principle:
"Two prisms
will have equal volumes if their bases have equal area
and their altitudes (heights) are equal."
Reflective Prisms
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In the study of optics, prisms
are used to reflect light, such as occurs in binoculars. Prisms
are also used to disperse light, or break light into its spectral
colors of the rainbow. The most commonly used optic prism is a
triangular prism, which has a triangular base and rectangular sides.
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