Transcript 12-1 Prisms

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Prism – A polyhedron that has two identical
ends (bases) and all flat sides ( lateral faces)
Green – BASES
Other– LATERAL FACES
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Any segment joining the two planes that
contain both bases and is perpendicular to
both.
The dashed lines are
altitudes.
Adjacent lateral faces
intersect at the black solid
lines called LATERAL
EDGES.
In some prisms lateral
edges are also altitudes,
BUT NOT ALWAYS.
LATERAL EDGES are all
parallel.
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The height of the prism is the length of the
altitude, not necessarily a vertical distance.
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A right prism is any prism in which the lateral
faces are all rectangles.
In right prisms the lateral edges are also
altitudes.
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Prisms in which the lateral faces are not
rectangles (i.e. parallelograms)
In this case the lateral edges are not altitudes.
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Most generally prisms are classified by right or
oblique, and then further classified by the
shape of the base faces.
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The surface area of a solid is measured in square
units.
The Lateral Area (L.A.) – of a prism is the sum of the
areas of its lateral faces.
The Total Area (T.A.) – is the sum of the areas of all
the faces. Sometimes referred to as just Surface Area
B denotes the area of a base
(total area or surface area ) T.A. = L.A. + 2B
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Total area refers to total surface area.
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L.A. = ah + bh + ch + dh + eh
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=(a+b+c+d+e)h
=perimeter * h
=ph
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Find the Surface Area
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Find the lateral area, surface area.
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Name the prism
How many lateral faces
Name 2 lateral edges
Name an altitude
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CD = 7, find the L.A, T.A.
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Find the Surface Area using formulas.
Cylinder
A
solid that has two congruent bases that are both
circles.
 An altitude of a cylinder is the perpendicular
segment connecting the two circular bases. The
height is the length of the altitude, not necessarily a
vertical distance.
 Find
the lateral area
 Use the lateral area to find the total area