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# 12.3 Surface area of Prisms PowerPoint PPT Presentation

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

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.

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.

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

• 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

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