Honors Geometry 1a. Homework Answers for Section 12.1 Find the total surface area of the right rectangular prism shown
AS = 2( 15• 5) + 2( 15• 10) + 2( 5• 10)
= 150 + 300 + 100 = 550 cm 2
10 cm
15 cm
5 cm
1b. Find the total surface area of the right rectangular prism shown
AS = 2( 12• 7) + 2( 12• 3) + 2( 7• 3)
= 168 + 72 + 42 = 282 mm 2
3 mm
12 mm
7 mm
1c. Find the total surface area of the right rectangular prism shown
AS = 2( 18• 9) + 2( 18• 9) + 2( 9• 9)
= 324 + 324 + 162 = 810 in2
9 in
18 in
9 in
2a. Find the lateral area of the triangular right prism shown
10
ALS = ( 3) ( 10) + ( 5) ( 10) + ( 7) ( 10)
3
5
7
Baroody = 30 + 50 + 70 = 150 u2
Page 1 of 5 Honors Geometry 2b. Homework Answers for Section 12.1 Find the lateral area of the triangular right prism shown
14
ALS = ( 2) ( 14) + ( 3) ( 14) + ( 4) ( 14)
2
= 28 + 42 + 56 = 126 u2
3
4
6a. Find the total area of the pieces of cardboard needed to construct the open box shown
8
7
AS = 2( 8) ( 6) + 2( 6) ( 7) + ( 8) ( 7)
6
= 96 + 84 + 56 = 236 u2
6b. Find the total area of the pieces of cardboard needed to construct the open box shown
AS = 3 sides + triangular bottom
30°
60°
= ( 8) ( 6) + ( 8) (6 3 ) + ( 8) ( 12) +
8
1
2
( 6) (6 3 )
12
30°
6 3
60°
6
= 48 + 48 3 + 96 + 18 3 = 144 +66 3 u2
7a. 6
Find the lateral area and the total area of the square right prism shown
ALS = 4( 6) 20 = 480 u2
ATS = 4( 6) 20 + 2( 6) 6 = 552 u2
6
Baroody 20
Page 2 of 5 Honors Geometry 7b. Homework Answers for Section 12.1 Find the lateral area and the total area of the triangular right prism shown
ALS = ( 3) 10 + ( 5) 10 + ( 4) 10 = 120 u2
4
3
ATS = 120 + 2
10
5
[
1
2
( 3) ( 4)
]
= 120 + 12 = 132 u2
7c. Find the lateral area and the total area of the isosceles triangular right prism shown
13
5
13
12
13
ALS = ( 13) ( 50) + ( 13) ( 50) + ( 24) ( 50) = 2500 u2
50
24
ATS = 2500 + 2
[
1
2
( 24) ( 5)
]
= 2500 + 120 = 2620 u2
7d. Find the lateral area and the total area of the regular hexagonal prism shown
10
6
6
6
6
6
Baroody ALS = 6( 6) ( 10) = 360 u2
6
[ ( )]
ATS = 360 + 2 6
62 3
4
= (360 + 108 3 ) u2
Page 3 of 5 Honors Geometry 8. Homework Answers for Section 12.1 Find the area of the right prism shown
ATS = 2( 7) ( 2) + 2( 2) ( 6) + ( 7) ( 6) + ( 4) ( 7) + ( 7) ( 5) + 2( 5) ( 2) + ( 7) ( 7)
2
4
7
5
2
7
7
7
2
= 28 + 24 + 42 + 28 + 35 + 20 + 49 = 226 u2
2
9. Find the lateral area and the total area of the right prism shown
ALS = 2( 11) ( 13) + 2( 11) ( 15)
15
15
13
13
= 286 + 330 = 616 u2
AB = 4( 16( 16 - 15) ( 16 - 13) ( 16 - 4) )
= 4( 24) = 96 u2
11
4
ATS = ALS + AB
= 616 + 96 = 712 u2
10. The perimeter of the scalene base of a pentagonal right prism is 17, and a lateral edge of the prism
measures 10. Find the prism's lateral area.
B
A
C
D
E
10
Baroody PABCDE = 17
ALS = ( 17) ( 10) = 170 u2
Page 4 of 5 Honors Geometry 11. Homework Answers for Section 12.1 A 6-inch cube is painted on the outside and cut into 27 smaller cubes.
a. How many of the small cubes have
Six faces painted?
0
Five faces painted?
0
Four faces painted?
0
Three faces painted?
8
Two faces painted?
12
One face painted?
6
No face painted?
1
b. If one of the small cubes is selected at random, what is
the probability that it has at least two painted faces?
8 + 12
27
=
6
6
6
20
27
c. What is the total area of the unpainted surfaces?
Top Layer - 3 + 4 + 3 + 4 + 3 + 4 + 3 + 4 + 5 = 33 faces
Bottom Layer - 33 faces
Middle Layer - 4 + 5 + 4 + 5 + 4 + 5 + 4 + 5 + 6 = 42 faces
⇒ 108 total faces are unpainted. Each face is 2in by 2in.
∴ total unpainted area is ( 108) ( 4 in2) = 432 in2
Baroody Page 5 of 5