Honors Geometry 5. Homework Answers for Section 9.8 Given:
Regular square pyramid PAMID with slant height PR, altitude PY
ID = 14
PY = 24
Find:
a.
b.
c.
d.
e.
AD
YR
PR
The perimeter of base AMID
A diagonal of the base (not shown)
Since the base is a square, AD = 14
P
24
M
I
A
Y
14
R
D
Since YR is half of ID, YR = 7
PR =25 (hypotenuse of 7-24-25
)
PAMID = 4(14) = 56
Since ID = AD and ∠IDA is right, AI (a diagonal of the base) = 14 2
6. Find the slant height of a regular square pyramid if the altitude is 12 and one of the sides of the square
base is 10.
P
Since YR is half of ID, YR = 5
12
PR = 13 (hypotenuse of 5-12-13
M
I
Baroody A
Y
10
)
R
D
Page 1 of 4 Honors Geometry 13. Homework Answers for Section 9.8 ABCDEFGH is a rectangular solid.
A
a. If face diagonal CH measures 17, edge GH measures 8,
and edge FG measures 6, how long is diagonal AG?
CG = 15 = AE (8-15-17
EG = 10 (6-8-10
AG =
C
15
)
)
(15)2 + (10)2 =
D
B
8E
325 = 5 13
F
17
10
6
G
A
EG = 30 (leg of 3-4-5 family
FG =
(30)2 - (3)2 =
H
D
B
b. If diagonal AG measures 50, edge AE measures 40, and
edge EF measures 3, how long is edge FG?
8
C
40
)
891 = 9 11
3E
F
50
30
H
G
14. PADIM is a regular square pyramid. Slant height PR measures 10,
and the base diagonals measure 12 2 .
a. Find ID
Since the base diagonal is 12 2 ,
ID = AD = 12 (legs of 45-45-90 )
b. Find the altitude of the pyramid
P
Since ID = 12
YR = 6
∴ PY = 8 (leg of 6-8-10 )
10
c. Find RD
RD =
1
AD =
1
(12) = 6
2
2
d. Find PD (length of a lateral edge)
PD =
Baroody (10)2 + (6)2 =
136 = 2 34
I
M
12 2
A
Y 6
12
6R
12
D
Page 2 of 4 Honors Geometry 17. Homework Answers for Section 9.8 The perimeter of the base of a regular square pyramid is 24. If the slant height is 5, find the altitude.
P
Since PAMID = 24, ID = 6 and YR = 3
Since PR = 5 (slant height), PY (the altitude) = 4
(3-4-5 )
M
A
Y
I
R
D
18. In the cube, find the measure of the diagonal in terms of x if:
In the cube, find the measure of the diagonal in terms of x if:
a. AB = x
Q
Since
ABC is isosceles right, AC = x 2
x
QC =
x2 + (x 2 )2 =
x2 + 2x2 =
A
3x2 = x 3
x
B
x
b. AC = x
Since
QC =
Baroody C
Q
ABC is isosceles right, AC =
x2 +
( )
x 2
2
2
=
x2 +
2x2
4
=
x
x 2
2
2x2 + x2
2
=
3x2
2
=
x 3
2
( )
2
2
=
C
x 2
A
2 B
x 6
2
Page 3 of 4 Honors Geometry 19. Homework Answers for Section 9.8 Find a formula for the length of a diagonal of a rectangular solid (use a, b, and c for the three dimensions)
x=
b2 + c2
d=
a2 +
(
b2 + c2 ) =
2
a
d
a2 + b2 + c2
x
b
Baroody c
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