Transcript 9-1A Surface Area of Prisms

12-2 Surface Area of Prisms
You found areas of polygons.
• Find lateral areas and surface areas of
prisms.
• Find lateral areas and surface areas of
cylinders.
Definition
A prism is a polyhedron with two identical polygonal
faces called bases that lie in parallel planes.
The other parallelogram-shaped faces are lateral
faces.
Where lateral faces intersect are lateral edges.
The altitude is a perpendicular segment that joins the
planes of the bases.
The height is the length of the altitude
Altitude or Height?
An altitude of a prism is a segment
perpendicular to both bases whose
endpoints are in the planes of the bases.
The length of an altitude is the height of the
prism.
Altitude
Right or Oblique?
Right prism—the lateral edges of the
prism are perpendicular to its bases.
Oblique prism---the lateral edges of the
prism are not perpendicular to its bases.
Classify each prism.
Lateral Area
Sides only
No bases
b
Lateral Area
Lateral area is the sum of the areas of the
lateral faces of a prism.
The lateral area of a right prism is the product
of the perimeter of its base and the height
of the prism.
L = Ph
p. 846
Find the lateral area of the regular hexagonal prism.
The bases are regular
hexagons. So the
perimeter of one base is
6(5) or 30 centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
Answer: The lateral area is 360 square centimeters.
Find the lateral area of the right
prism with right triangular bases.
Ask: What is the shape of
the base?
Triangle
Find the triangle LA formula
LA  s  s  s h
LA  6  8  109
LA  24(9)  216
8
6
10
9
Find the lateral area of the regular octagonal prism.
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Surface Area
The surface area of the prism is the total
area of all of its faces including the bases.
The surface area of a right prism is the sum
of its lateral area and the areas of its
bases.
S = L + 2B or S = PH+2B
p. 846
Surface Area
SA = P h + 2 B
or
Find the surface area of
the rectangular prism.
Surface area of a prism
L = Ph
Substitution
Simplify.
Answer: The surface area is 360 square centimeters.
Find the surface area of the right
prism with right triangular bases.
Ask: What is the shape of
the base?
Triangle
Find the triangle SA formula
8
6
10
9
SA  (6  8  10)(9)  2(1/2)(8)( 6)
SA  216  48  264
Find the surface area of the triangular prism.
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Lateral Area and Surface Area
Look at the top of your formula chart.
The first question you need to ask is:
What shape is the base?
Find the shape at the top. Then ask,
what kind of figure is it and go to that
formula.
There is a key for all of the abbreviations
at the bottom of the page.
12-2 Assignment
Page 850, 9-17
skip 10
NO FORMULAS WITH NUMBERS
NO CREDIT