12. 1 pd8
April 10, 2017
chapter 12 Surface Area and Volume of prisms, cylinders, pyramids,
cones, spheres and combinations of solids.
Solids whose faces are flat are called polyhedra
familiar polyhedra are prisms and pyramids.
f
a
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April 10, 2017
The "top and bottom" of the prism are congruent polygons,
called bases and the "sides" are rectangles, called lateral
faces. The lateral faces and the bases are all called faces.
In the figures below, the rt triangular prism has 5 faces and
the rt pentagonal prism has 7 faces.
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DEF: every prism has two parallel bases. The other flat surfaces are called
lateral faces. All together a prism has two bases and lateral faces, but all are
called faces in general
DEF: The lateral surface area of a prism is the area of the lateral faces
DEF: The total surface area of a prism is the lateral area plus the area of the
two bases.
20
Find the LA (lateral area)
and the TA (total surface area)
15
13
12
14
13
13
24
50
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6
Reg. Hexagonal prism
10
Find the total area of the right
prism, assume parallel lines and
right angles where appropriate.
4
2
7
2
2
5
7
7
7
2
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15
15
Find the lateral area and the total area
13
13
of the right prism shown
11
11
4
13
Find the total
surface area
13
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April 10, 2017
April 10, 2017
12. 1 pd8
12.2 surface area of Pyramids
net for a ? pyramid
A pyramid has only one base. IF the base is a regular polygon, then the pyramid is
called a regular pyramid. The vertex is the point where the lateral faces intersect (the
lateral edges intersect at the vertex as well. A pyramid is named by its base, ie., a square
pyramid, a hexagonal pyramid. The lateral faces are always isosceles triangles if the
pyramid is a regular pyramid.
Lateral area is the area of the lateral faces (triangles) and the total area is the lateral area
plus the area of the one base(square, triangle, hexagon, etc.
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altitude
slant height
slant edge
In section 9.8 we investigated some regular pyramids because of the
characteristics of the altitude. The foot of the altitude is the center of the base in
a regular pyramid. It is also the height of the pyramid. The slant height is the
height of any of the lateral faces.
For the square pyramid, find the lateral area
and the total area
12
10
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the pyramid shown has a rectangular base. Is it regular?
FInd the LA and the TA
25
25
25
14
30
This figure is a solid formed by a square prism
and a regular pyramid.
Is ABCD a face of the solid?
D
How many faces?
Find the TA
13
13
A
C
B
10
10
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PEFGH is a regular pyramid. Points A, B, C and D
are the midpoints of the lateral edges., PE = 10, EF = 12
P
Find the LA of PEFGH, LA of PABCD
The TA of PEFGH, the ratio of the areas of
DABC to HEFG and the area of TRAP ABFE
D
A
H
B
E
G
C
F
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KQVW is a square
with area 100
find the LA and SA
the base is a regular pentagon with edge
length 16 and the slant height is 20.
FInd the SA
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find TA
slant edge = 9
10
base edge =6