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