12-3 Surface Areas of Prisms

Kaitlin and Lauren Nelson

Objectives

Find the lateral area of prisms.

Find the surface area

of prisms.

Parts of a Prism

Bases- congruent faces in parallel planes

Lateral Faces- the faces that are not bases

Lateral Edges- where the lateral faces intersect. Are parallel segments

Altitude- Segment that is perpendicular to the bases. Is = height

base

lateral edge

lateral faces

altitude

Types of Prisms

Right Prism- prisms that have lateral edges that are also altitudes.

Oblique prism- prism with lateral edges that are not perpendicular to the bases

Lateral AreaThe lateral area of a prism, L, is the sum of the areas of the lateral faces.

L = ah+bh+ch+dh+eh+fhL= h(a+b+c+d+e+d+f)L = Ph

a b c d e f

h

EXAMPLE 1!!!!!EXAMPLE 1!!!!!

15 cm

20 cm

Find the lateral area of the regular hexagonal prism, please!

Lateral area = Perimeter x height

15 cm

20 cm

WORK IT OUT!WORK IT OUT!

L= Ph

L= [6(15)] 20

L= (90)(20)

L= 1800 cm2

Surface Area of Prisms

The surface area of a right prism is the lateral area plus the areas of the bases.

Surface area = L + 2B

EXAMPLE 2!!!!!Bartholomew wants to wrap his cheese wedge in tin foil because he forgot his great-uncle’s birthday and wants to make it up to his cheese-loving relative. Find the surface area of the cheese wedge so that Bartholomew knows how much tin foil he will need.

SA= L + 2B

8 cm6 cm

5 cm

6cm8 cm

5 cm

WORK IT OUT!WORK IT OUT!

62+ 82= c2

36+ 64= c2

100= c2

10= c

10 cmL= Ph

L= (6+ 8+ 10) 5

L= (24) 5

L= 120 cm2

A= ½ (6)(8)

A= ½ (48)

A= 24 cm2

SA= L+ 2B

SA= 120+ 2(24)

SA= 120+ 48

SA= 168 cm2

EXAMPLE 3!!!!! 3 ft 4 ft

2 ft

Pete’s dog, Chalupa con Queso, had an “accident” on his ottoman. If Pete doesn’t reupholster it with his girlfriend’s favorite fabric, she will leave him for a lumberjack with a cat. For Pete’s sake, (ha-ha) figure out the surface area of the ottoman that needs reupholstering.

4 ft

2 ft

3 ft WORK IT OUT!!L= Ph

L= [2(3)+ 2(4)] 2

L= (6 + 8) 2

L= (14) 2

L= 28 ft2

A= bh

A= (3)(4)

A= 12 ft2SA= L + B

SA= 28 + 12

SA= 40 ft2

Dedication

This spiffy-sweet PowerPoint is dedicated to you, you wonderful people…you, for saving Pete’s pride and making Ivan the lumberjack eat flap-jacks with only his cat to keep him company.

Drum roll, please…

Your lovely assignment is…. I hate spelling the word “assignment”. I always get it wrong and I feel like I'm cussing while I type.

Oh, my bad. Here you go.

Page 651 #6-12,14, 16-21 (Relax people! It’s only fourteen problems. Don’t be

hatin’)