Ch 5, 6, 8, 9 and 10 Review for Final Exam
Page 1
Name ___________________________________
Note: Drawings are NOT drawn to scale! Do not approximate answers unless indicated!!
1. x = _____
2. Find the measure of one exterior angle of a regular
decagon.
360/10 = 36
Top ∆:
5:12:13 → 10:24:26
missing leg 10 (hyp of
bottom ∆).
Bottom ∆:
3:4:5 → 6:8:10
So x = 8
3. Find each unknown angle or arc.
4. Area = 126 in2 b = _____.
central angle = arc: a = 95.
1
A = h ( b1 + b2 )
2
1
126 = ( 9 )( b + 16 )
2
126 = 4.5 ( b + 16 )
linear pair: b = 180 – 95 = 85
b = 85
radii of ○ ≅ , so ∆ isos.
180 – 85 = 95
95/2 = 47.5
c = 47.5
5. Find the measure of one interior angle of a regular
28 = b + 16
b = 12 cm
6. KLMN is a square and NM = 8.
octagon.
(8 – 2) 180 = 1080
1080/8 = 135
m∠OKL = 45
m∠MOL = 90
Perimeter
KLMN = 32_
S. Stirling
Ch 5, 6, 8, 9 and 10 Review for Final Exam
Page 2
1. Find the area of right isosceles triangle if a leg
measures 8 cm. Find the length of the 3rd side
of the triangle.
Name ___________________________________
2. Bert’s Bigtime Bakery has baked the world’s largest chocolate
cake. It is a rectangular sheet cake that is 600 cm by 400 cm by 180
cm high. Bert wants to apply frosting to the four sides and the top.
How many liters of frosting does he need if 1 liter of frosting covers
about 1200 cm2?
missing side
Area triangle:
c2 = a2 + b2
A = 1 bh
2
1
 
A =   ( 8)( 8 ) = 32 cm2
2
c 2 = ( 8) + ( 8 )
2
2
1) surface area:
front & back:
2i600i180 = 216,000
c 2 = 128
right & left:
c = 128 ≈ 11.31
top:
2) frosting:
600, 000
= 500 liters
1200
2i400i180 = 144,000
400i600 = 240, 000
Total = 600,000
3. A cone has volume 320π cm3 and height 16 cm.
Find the radius
of the base.
Round your
answer to 2
decimal places.
4. Rectangular pyramid OP = 6. V = __
1
V = Bh
3
1
320π = (π r 2 ) (16 )
3
16π 2
320π =
r
3
320π
3
3 16π 2
r
•
=
•
1
16π 16π
3
60 = r 2
1
V = Bh
3
1
V = ( 8i5)( 6 )
3
V = 80 units3
r = 60 ≈ 7.75
5. The diameter is 40. Length of
AC = _____
6.
a = 30 _
inscribed angle = ½ arc
AC = 100
b = 37
Arc length = fraction of C.
x = 49
100
i2π ( 20 ) =
360
10
100
iπ (10 ) =
π
9
9
≈ 11.11π or 34.91
S. Stirling
y = 131
Ch 5, 6, 8, 9 and 10 Review for Final Exam
1. x = ______
Page 3
2. If C = 36π cm, A = _____.
x2 = a 2 + b2
x 2 = (14 ) + (14 )
2
2
x 2 = 392
x
Name ___________________________________
x = 392 ≈ 19.80
Circumference:
C = 2π r
36π = 2π r
36π
r=
= 18
2π
4.
3. SA = __ V = __
Area:
A = π r2
A = π (18)2
A = 324π cm2
Volume = __ You may approximate.
Surface Area:
A = 4π r 2
A = 4π (6) 2
A = 144π units2
Volume:
(π r ) h + 12  34 π r



14
2
3
= (π (5) ) (8) +  π (5) 
2 3

= 628.32 + 261.80
890.12 units3
2
Volume:
4
V = π r3
3
4
3
V = π ( 6)
3
V = 288π units3
3
6. ABCD is a rhombus, AD = 10, AC = 16 and DO = 6.
5. a = ___, b = ___, c = ___
Inscribed angle = ½ arc
1
c = ( 70 ) = 35
2
1
a = (180 ) = 90
2
Triangle sum = 180
180 – 35 – 90 = 55 = b
S. Stirling
V = bottom + top
OB = 6_
m∠AOD = 90
BC = 10_
AO = 8_
Ch 5, 6, 8, 9 and 10 Review for Final Exam
1. SA = __
Right triangle:
Page 4
Name ___________________________________
2. V = __
a 2 + b2 = c2
(6) 2 + (12) 2 = c 2
c 2 = 36 + 144 = 180
c = 180 ≈ 13.42
Volume:
1
(π r 2 ) h
3
1
V = (π (6) 2 ) (12)
3
V = 144π units3
V=
Surface Area:
A = π r 2 + π rl
A = π (6)2 + π (6)(13.42)
A = 113.10 + 252.96
A ≈ 366.06 units2
3. ABCD is a parallelogram.
4. s =12 cm, a = 14.5 cm, A = _____
a = 51 _
1
A = ans
2
1
A = (14.5)(8)(12)
2
A = 696 cm2
b = 48
c = 70
5. Rectangle ABCD has area 2684 m2 and width
44 m. Find its Find its perimeter.
A = bh
2684 = b(44)
b = 61 m
P = 2(44) + 2(61)
= 210
S. Stirling
6. Find the area. Round answers to two decimal
places.
3.71
A = bh
A = (13.4)(3.71)
A = 49.69 cm2
Ch 5, 6, 8, 9 and 10 Review for Final Exam
Page 5
1. Right trapezoidal prism SA = __ V = __
Surface Area:
4
SA = 2 B + ph
1

SA = 2  (4)(3 + 6)  + (18)(8)
2

SA = 180 units2
Name ___________________________________
2. ABCD is a rhombus
m∠ADC = 146 .
m∠ABO = 73
m∠DCB = 34
m∠OAB = 17
Volume:
V = Bh
1

V =  (4)(3 + 6)  (8)
2

V =144 units3
4. SA = __ V = __
Surface Area:
SA = 2 B + ph
AD is a tangent. AC is a diameter. m∠A = ___,
mAB = ___, m∠C = ___, mCB = ___,
3.
⊥ radii
m∠A = 90
tangent
∆ sum
m∠C = 90 − 54 = 36
SA = 2 π (4)2  + (2π i4)(8)
SA = 96π units2
Volume:
V = Bh
V = π (4)2  (8)
V = 128π units3
mAB = 72
inscribed angle = ½ arc
mCB = 180 − 72 = 108
6. Find the area of the shaded sector.
Shaded:
360 – 120 = 240
5. Find the area. Round to 2 decimal places.
Right triangle:
a 2 + b2 = c2
(3) 2 + b2 = (7)2
b2 = 40
b = 40 = 2 10 ≈ 6.32
A = 1 bh
2
A = 1 (6)(6.32)
2
A = 18.96 ft2
S. Stirling
a
π r2
360
240
A=
π (4)2
360
32
A = π ≈ 134.04 cm2
3
A=
7. If the diagonals of a quadrilateral are perpendicular
bisectors of each other, then the quadrilateral must be a
_____. (Give the best answer).
Rhombus. Not square, since this statement is true for all
types of rhombi.
Ch 5, 6, 8, 9 and 10 Review for Final Exam
Page 6
Name ___________________________________
4. If the diagonal of a rectangle is 26 and one side is 10,
1. V = __
what does the other side measure?
5: 12: 13
10: 24: 26 so the side is 24.
OR
262 = 102 + b2
Volume:
1 4
1 4
V = i π r 3 = i π (3)3 = 18π units3
2 3
2 3
676 = 100 + b 2
b = 576 = 24
5. The diagonals of a rhombus measure 6 and 8, what is the
2. PQRS is a rectangle and OS = 16.
measure of the side of the rhombus.
OQ = 16_
Diagonals are bisected and form 4 congruent right triangles
with legs 3 and 4.
3: 4: 5 right triangles
m∠QRS = 90
So the side would measure 5.
OQ = 32_
6. Is a triangle with sides that measure 11, 36 and 48 a right
3. The circumference is 24π and
Length of .
CD = ___
mCD = 60° .
Arc length = fraction of C.
60
i24π =
360
1
i24π = 4π units
6
triangle? (Yes or No.)
No, it isn’t a triangle at all.
11 + 36 = 47 which is less than 48.
7. Is a triangle with sides that measure 9, 40 and 41 a right
triangle? (Yes or No.)
Yes
This review sheet is intended to give you mixed
review from all of the chapters we have studied.
It does not cover every type of item you may be
faced with on the final. Please be sure to review
note sheets, worksheets, summary sheets and
homework assignments from past chapters.
Remember, you can find materials on my
website if you cannot find your copy!
Also, review your area project!!
S. Stirling
412 = 402 + 92
1681 = 1600 + 81
1681 = 1681
8. If the diagonals of a quadrilateral are equal and bisect
each other, then the quadrilateral must be a _____. (Give
the best answer).
Rectangle. Not square, since this statement is true for all
types of rectangles