Download Geometry Spring Final Review

Geometry Spring Final Review
4th Six Weeks:
I.
Complete the chart. MAKE SURE YOU KNOW THE FORMULAS FOR THE TEST!
Type of Polygon
Interior Angle Sum
Measure of EACH
Exterior Angle Sum
Measure of EACH
Interior Angle
Exterior Angle
1.
150
2.
18
3.
1260
II.
Quadrilaterals. Find the requested information.
4. Square with Perimeter of 80
5. Rectangle
x
A
5x
y
B
z
n°
3y+2
E
2z+10
x
M
Q
d°
5x-9
b°
29
N
e°
A
F
a
CF
AB 
B
3a+1
m°
CF 
p°
88
q°
4a+5
n°
DE 
C
m
n
64
6a+2
E
D
p
e
PL 
q
b°
9. Parallelogram
PN 
L
28°
a
M
N
6a-7
d
x
90
a
58
55
46°
°
75
b
c
17°
e °
A
Perimeter 
3a-2
c° f°
d°
4a+1
7. Trapezoid with midsegment
mMNP 
8. Kite
P
r
mMNR 
P
2a+2
d
q
C
c
R
n
r°
D
a
b
m
BC=12
CD=16
p°
MN 
Perimeter 
c°
a°
p
C
DE 
74
E
n
6. Rhombus
3x-1
q°
m
p°
AC 
B
m°
n°
AD 
m°
D
A
BD 
d
D
c
b
f
38
5y
e
C
B
5x
y
BC 
CD 
Perimeter 
a
b
e
c
mLPN 
d
e
f 
III.
More Polygons.
10. If the interior angle sum of a polygon is 1080 ,
what kind of polygon is it?
IV.
11. If the exterior angle measure of a polygon is
30 , what is its exterior angle sum?
Ratios and Proportions.
12. Solve for
x.
13. The sides of a quadrilateral are in
the ratio 2:3:5:6. The perimeter of
the quadrilateral is 272 feet. Find
the length of each side.
2x 1 5

3x  2 2
14. The interior angles of a triangle
are in the ratio 2:3:5. Find the
measure of each angle.
V. Review Pythagorean Theorem, Special Right Triangles and Triples! This is 5-7 and 5-8 in your textbook.
See page 365 and 369 for sample problems.
5th Six Weeks:
I.
Find the area of the following figures. REMEMBER… if you use a triple, write “TRIPLE.”
1. RHOMBUS.
2. KITE.
10
6
16
17
Perimeter = 68 inches
3. ISOSCELES TRIANGLE.
4. ISOSCELES TRAPEZOID.
11
13
12
5
5
5. PARALLELOGRAM.
6. RECTANGLE.
17
10
12
6
6
20
16
22
7. REGULAR HEXAGON.
8. CIRCLE.
18
Diameter = 12
II.
SHOW YOUR WORK. Find the lateral area, total area, and volume for each figure.
9. Right Cone with Base of Area 108 square
10. Right Cylinder with Base Circumference =
inches.
meters
LA = _________
B = __________
TA = _________
V = __________
8 root 3
11. Regular Pyramid with Slant Height = 10 feet and
Apothem = 6 feet
LA = _________
B = __________
TA = _________
V = __________
LA = _________
B = __________
TA = _________
V = __________
19
12. Regular Square Pyramid
LA = _________
B = __________
TA = _________
V = __________
12 inches
18 inches
13. Cube with an edge of 5.
LA = _________
B = __________
TA = _________
V = __________
14. Sphere with a diameter of 20 inches.
LA = _________
B = __________
TA = _________
V = __________
16
III.
SHOW YOUR WORK.
15. Find the height of a right cylinder whose total
area is 279 square meters and whose radius is 11
meters.
16. Find the total area of a cube whose volume is
64 cubic inches.
17. Find the radius of a sphere if the surface area
of the sphere is 784 square inches.
18. Find the height of a right cone if its radius is
feet and its lateral area is 544 square feet.
16
6th Six Weeks:
I.
Find the requested information. SHOW YOUR WORK.
1. Find the area of the sector (shaded). Leave your 2. Find the area of the circle segment (shaded).
answer in terms of  .
Round your answer to the nearest tenth.
240 degrees
15 cm
9 in
Asegment  ____________
Asector  ____________
» . Round your answer
3. Find the LENGTH of CD
to the nearest hundredth.
OP and MP are tangents to e N .
O
9
192 degrees
C
5x-3
D
y  _____
PN  _____
4y
LCD
»  ____________
5.
x  ______
N
6
P
7 ft
M
OP  _____
6.
S
C
60
82
T
x  ______
B
G
»  ______
mAB
8.
129
»  ______
mGC
D
mABC  ______
B
ј
mSUR
 ______
7.
79
A
x  ______
ј
mTSU
 ______
y
U
(15x)
y  ______
R
x
39
x  ______
x
A
4.
145
A
B
26
34
D
C
C
x
E
x  ______
»  ______
mDE
9.
DG and FG are tangents of E .
x  ______
D
»  ______
mDF
C
E x
10.
70
J
x
ј
mDCF
 ______
52 G
mKLH  ______
87
L
mDCF  ______
F
H
78
I
11.
x  ______
Q
12.
mWVT  ______
U
y  ______
y
»  ______
mUV
mNPO  ______
N
P
x  ______
є  ______
mJI
K
(3x+5)

W
»  ______
mNO
36
76
(5x-9)
V
O
R
13.
AY  ______
T
14.
AC  ______
279
8
C2
m»
AB  ______
Z
mIBH  ______
5x-3
A
AB  ______
B
Y
x  ______
I
B
H
J
260
»  ______
mHI
G
22
100
mAYZ  ______
A
II.
15.
Find the requested trigonometric ratios using the given right triangle.
16.
B
5
3
sin C 
cos B 
cos C 
tan B 
tan C 
C
A
III.
sin B 
E
15
8
D
sin D 
sin F 
cos D 
cos F 
tan D 
tan F 
F
Draw and label a right triangle. Then find the requested ratio.
17. If sin C 
7
, then find cos C .
25
18. If tan B 
12
, then find sin B .
5
IV.
Solve for the variable(s). Round lengths to the nearest tenth and angles to the nearest degree. Be
sure to give your equation in calculator-ready form BEFORE you get your answer.
20.
21.
19.
x
16
V.
22.
20
42
x
10
64°
x
17
Solve each triangle. Round lengths to the nearest tenth and angles to the nearest degree.
23.
24.
F
m
g
B
p
F
C
M 
f
M
A
B
73°
G
a
30
25
21
g
15
f 
a
C
61°
p
P
m
N
H
VI.
WORD PROBLEMS.
25. Find the angle of elevation if a 45-foot flagpole casts a shadow 63 feet long. Answer to the nearest
degree.
26. An observer on the ground is 1.5 miles from a building that is 1600 feet tall. What is the angle of
depression from the building to the observer?
27. A kite is flying at an angle of elevation of about 62 degrees. The entire length of the string has been
let out. The height of the kite above the ground is 40 meters. How much string has been let out?
28. A certain jet is capable of a steady 16 degree climb. How much altitude does the jet gain when it
moves 1 kilometer through the air? Answer to the nearest 50 meters.