Transcript Slide 1

Geometry
12.1
Prisms
Prisms
Today you will learn how to find
three measurements about prisms. You
will find:
Lateral area:
L.A.
Total area:
T.A.
Volume:
V
Different Prisms
lateral faces are rectangles
Right
rectangular
prism
Right
hexagonal
prism
Lateral faces are
not rectangles
Oblique
triangular
prism
Prism Vocabulary
base
shaded faces
lie in parallel planes
congruent polygons
lateral faces
faces (not bases)
parallelograms that
intersect each other in
lateral edges
lateral edges
base
ecaf
face
base
Prism Vocabulary
altitude
segment that joins the two
bases. It is perpendicular
to both.
In a right prism, the lateral edges
are altitudes
height
the length of an altitude
referred to as H
lateral area
sum of the areas
of the lateral faces
+
+
+
back
front
To find lateral area (L.A.): Find the perimeter of the base
Multiply it by height
H
H
width
H
+
length
H
+
width
H
+
length
= PERIMETER
To find total area (T.A.):
Add the lateral area (L.A.)
With the area of the 2 bases
length
length
Lateral Area of a Prism: L.A.
The lateral area of a right prism equals the
perimeter of a base times the height of the
prism.
L.A = pH
8
6
4
LA = [2(6) +2(4)] • 8
= 160 square units
Total Area of a Prism: T.A.
The total area of a right prism equals the
lateral area plus the areas of both bases.
T.A = L.A. + 2B
8
6
4
TA = 160 + 2(6 • 4)
= 160 + 48
= 208 square units
Exercises
Find the (a) lateral area and (b) total area of each right prism.
9 cm
9
cm
4 cm
base = 9(4)
1. (a) LA = pH
LA = [2(9) + 2(4)] (9)
LA = 234 cm²
(b) TA = LA + 2B
5
12
2
0
base = ½(5)(12)
2. (a) LA = pH
LA = [5 + 12 + 13] (20)
LA = 600
(b) TA = LA + 2B
TA = 234 + 2(36)
TA = 600 + 2[(½)(5)(12)]
TA = 306 cm²
TA = 660
Exercises
Find the (a) lateral area and (b) total area of each right prism.
10 cm
13 cm
3. (a) LA = pH
13 cm
20 cm
H = 20
20 cm
LA = (56)(20)
LA = 1120 cm²
(b) TA = LA + 2B
10
13
12
5
20
13
5
Base is a trapezoid
TA = 1120 + 2(180)
P = 10 + 20 + 13 + 13
= 56
A = hm
A = 12•15 = 180
TA = 1480 cm²
To find volume (V):
Find the area of the base
Multiply it by height
H
length
Volume of a Prism: V
The volume of a right prism equals the area of a
base times the height of the prism.
V = BH
8
6
4
V = (6 • 4) • 8
= 192 cubic units
Exercises
7.
8.
9.
10.
l
25
8
15
8
w
20
4
12
6
H
10
6
4
12
900
144
216
336
1900
5000
208
576
432
192
720
576
L.A.
T.A.
V
TA = LA + 2B
9. 216 = 4p
= 216 + 2(15•12)
p = 54
= 216 + 360
54 = 2(15) + 2w
= 576
2w = 24
V = BH = (15•12) • 4 = 720
w = 12
10. V = BH
LA = pH
= [2(8) + 2(6)] • 12
= 336
576 = 48H
H = 12
TA = LA + 2B
= 336 + 2(8•6) = 336 + 96 = 432
Homework
pg. 477 CE #1-10
WE #1-25 odd