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’)