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.
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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
b
Sides only
No bases
Lateral AreaLateral 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.
Answer: The lateral area is 360 square centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
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
hsss LA
91086LA 21624(9)LA
68
10
9
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Find the lateral area of the regular octagonal prism.
Surface AreaThe 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.
Answer: The surface area is 360 square centimeters.
Surface area of a prism
L = Ph
Substitution
Simplify.
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
6)2(1/2)(8)(10)(9)8(6SA
68
10
9
26448216SA
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Find the surface area of the triangular prism.
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 NUMBERSNO CREDIT
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