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12.3 Surface area of Prisms. Objectives. Find lateral areas of different types of prisms Find the surface areas of prisms. Vocabulary. Lateral faces - the faces that are not bases of the prism

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12.3 Surface area of Prisms

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12.3 Surface area of Prisms


Objectives

  • Find lateral areas of different types of prisms

  • Find the surface areas of prisms


Vocabulary

  • Lateral faces- the faces that are not bases of the prism

  • Lateral edges- lateral faces share lateral edges. Lateral edges are the parallel bases connecting the bases.

  • Lateral area- the sum of the areas of the lateral bases or find the perimeter of the base and multiply times height of lateral edge.


Example

Lateral edge

Lateral face

Base


Vocabulary

  • Right prism- a prism with lateral edges that are also altitudes. The lateral edges are perpendicular to each base.

  • Oblique prism- a prism in which the lateral edges are not perpendicular.


Example

Oblique prism

Right prism


How to find Lateral Area

a

b

c

d

e

f

h

L = ah + bh + ch + dh + eh + fh


Example

16

Find the lateral area of the prism.

10

10

11


Answer

  • First multiply lateral edge by all three base sides.

  • 10(16) + 10(16) + 11(16) = lateral area

  • 160 + 160 + 176 = lateral area

  • 496 square units = lateral area

16

10

10

11


Key Concept Lateral area of prisms

  • If a right prism has a lateral area of L square units, a height of h units, and each base has a perimeter of P units, then L=Ph

P

h


Example

6

Find the lateral area of the cube using the last key concept.

6


Answer

6

(6 + 6 + 6 + 6)6 = Lateral area

(24)6 = Lateral area

144 = Lateral area

6


Key Concept Surface area of prisms

If the surface area of a right prism is T square units, its height is h units, and each base has an area of B units and a perimeter of P units, then T = L + 2B

h


Example

Amber went to the store to look for sheets for her bed. Amber’s bed is 5 meters long and 3 meters wide. The mattress is 1 meters high. What is the surface area of her bed so she can find the right size sheets?


Example

Amber went to the store to look for sheets for her bed. Amber’s bed is 5 meters long and 3 meters wide. The mattress is 1 meters high. What is the surface area of her bed so she can find the right size sheets?

The surface area was 15 meters squared.


Homework

  • Pre-AP Geometry

    Pg 651 # 6-24 all, 29-33 all


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