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

10 10

11

Find the lateral area of the prism.

Answer

16

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

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

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

6

6

Answer

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

(24)6 = Lateral area

144 = Lateral area

6

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