Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
1111
© Glencoe/McGraw-Hill vii Glencoe Geometry
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 11. As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
apothem
geometric probability
irregular figure
irregular polygon
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Geometry
Vocabulary Term Found on Page Definition/Description/Example
sector of a circle
segment of a circle
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
1111
Learning to Read MathematicsProof Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
1111
© Glencoe/McGraw-Hill ix Glencoe Geometry
Proo
f Bu
ilderThis is a list of key theorems and postulates you will learn in Chapter 11. As you
study the chapter, write each theorem or postulate in your own words. Includeillustrations as appropriate. Remember to include the page number where youfound the theorem or postulate. Add this page to your Geometry Study Notebookso you can review the theorems and postulates at the end of the chapter.
Theorem or Postulate Found on Page Description/Illustration/Abbreviation
Postulate 11.1
Postulate 11.2
Postulate 11.3Area Probability Postulate
Skills PracticeArea of Parallelograms
NAME ______________________________________________ DATE ____________ PERIOD _____
11-111-1
© Glencoe/McGraw-Hill 613 Glencoe Geometry
Less
on
11-
1
Find the perimeter and area of each parallelogram. Round to the nearest tenth ifnecessary.
1. 2.
3. 4.
5. 6.
Find the area of each figure.
7. 8.
COORDINATE GEOMETRY Given the coordinates of the vertices of a quadrilateral,determine whether it is a square, a rectangle, or a parallelogram. Then find thearea of the quadrilateral.
9. A(!4, 2), B(!1, 2), C(!1, !1), 10. P(!3, 3), Q(1, 3), R(1, !3),D(!4, !1) S(!3, !3)
11. D(!5, 1), E(7, 1), F(4, !4), 12. R(2, 3), S(4, 10), T(12, 10),G(!8, !4) U(10, 3)
8
222
2 2
2
263
3
4
6
6
1
1
1
1122
22
1
18.5 km
9 km
3.4 m
26 in.
22 in.
45!
14 yd
7 yd45!
5.5 ft
4 ft
60!
20 cm
30 cm60!
© Glencoe/McGraw-Hill 614 Glencoe Geometry
Find the perimeter and area of each parallelogram. Round to the nearest tenth ifnecessary.
1. 2. 3.
Find the area of each figure.
4. 5.
COORDINATE GEOMETRY Given the coordinates of the vertices of a quadrilateral,determine whether it is a square, a rectangle, or a parallelogram. Then find thearea of the quadrilateral.
6. C(!4, !1), D(!4, 2), F(1, 2), G(1, !1) 7. W(2, 2), X(1, !2), Y(!2, !2), Z(!1, 2)
8. M(0, 4), N(4, 6), O(6, 2), P(2, 0) 9. P(!5, 2), Q(4, 2), R(5, 5), S(!4, 5)
FRAMING For Exercises 10–12, use the following information.A rectangular poster measures 42 inches by 26 inches. A frame shop fitted the poster with ahalf-inch mat border.
10. Find the area of the poster.
11. Find the area of the mat border.
12. Suppose the wall is marked where the poster will hang. The marked area includes anadditional 12-inch space around the poster and frame. Find the total wall area that hasbeen marked for the poster.
7
7 3
3 43
1
333
3
2
2
22 8
922
2
22
2
1
1
4
4
4
10 in.
45!10 cm
8 cm
45!
5 m
11 m60!
Practice Area of Parallelograms
NAME ______________________________________________ DATE ____________ PERIOD _____
11-111-1
Skills PracticeAreas of Triangles, Trapezoids, and Rhombi
NAME ______________________________________________ DATE ____________ PERIOD _____
11-211-2
© Glencoe/McGraw-Hill 619 Glencoe Geometry
Less
on
11-
2
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2. 3.
Find the area of each quadrilateral given the coordinates of the vertices.
4. trapezoid WXYZ 5. rhombus HIJKW(!5, 3), X(3, 3), Y(6, !3), Z(!8, !3) H(4, !3), I(2, !7), J(0, !3), K(2, 1)
Find the missing measure for each figure.
6. Trapezoid RSTU has an area of 7. Trapezoid JKLM has an area of 935 square centimeters. Find the 7.5 square inches. Find ML.height of RSTU.
8. Triangle ABC has an area of 9. Rhombus EFGH has an area of 1050 square meters. Find the 750 square feet. If EG is 50 feet,height of !ABC. find FH.
HE
F G
A C
B
60 m
M L
J K5 in.
2 in.
55 cmR U
TS 30 cm
34 cm28 cm
21 cm
40 cm
22 in.
12 in.25 in.
4 ft 3.5 ft6 ft
© Glencoe/McGraw-Hill 620 Glencoe Geometry
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3.
Find the area of each quadrilateral given the coordinates of the vertices.
4. trapezoid ABCD 5. rhombus LMNOA(!7, 1), B(!4, 4), C(!4, !6), L(6, 8), M(14, 4), N(6, 0),D(!7, !3) O(!2, 4)
Find the missing measure for each figure.
6. Trapezoid WXYZ has an area of 7. Triangle PRS has an area of 13.75 square meters. Find WX. 68 square yards. If the height of !PRS
is 8 yards, find the base.
DESIGN For Exercises 8 and 9, use the following information.Mr. Hagarty used 16 congruent rhombi-shaped tiles to design themidsection of the backsplash area above a kitchen sink. The length of the design is 27 inches and the total area is 108 square inches.
8. Find the area of one rhombus.
9. Find the length of each diagonal.
P S
R
Z Y
W X
3.5 m
2.5 m
37 ft 22 ft 26 ft
10 cm
3 cm6 cm3.5 cm
4 m
2.6 m1.5 m
3.2 m
Practice Areas of Triangles, Trapezoids, and Rhombi
NAME ______________________________________________ DATE ____________ PERIOD _____
11-211-2
Skills PracticeAreas of Regular Polygons and Circles
NAME ______________________________________________ DATE ____________ PERIOD _____
11-311-3
© Glencoe/McGraw-Hill 625 Glencoe Geometry
Less
on
11-
3
Find the area of each regular polygon. Round to the nearest tenth.
1. a pentagon with a perimeter of 45 feet
2. a hexagon with a side length of 4 inches
3. a nonagon with a side length of 8 meters
4. a triangle with a perimeter of 54 centimeters
Find the area of each circle. Round to the nearest tenth.
5. a circle with a radius of 6 yards
6. a circle with a diameter of 18 millimeters
Find the area of each shaded region. Assume that all polygons are regular. Roundto the nearest tenth.
7. 8.
9. 10.
5 cm4 ft
8 m
4 m
3 in.
© Glencoe/McGraw-Hill 626 Glencoe Geometry
Find the area of each regular polygon. Round to the nearest tenth.
1. a nonagon with a perimeter of 117 millimeters
2. an octagon with a perimeter of 96 yards
Find the area of each circle. Round to the nearest tenth.
3. a circle with a diameter of 26 feet
4. a circle with a circumference of 88 kilometers
Find the area of each shaded region. Assume that all polygons are regular. Roundto the nearest tenth.
5. 6.
7. 8.
DISPLAYS For Exercises 9 and 10, use the following information.A display case in a jewelry store has a base in the shape of a regular octagon. The length ofeach side of the base is 10 inches. The owners of the store plan to cover the base in blackvelvet.
9. Find the area of the base of the display case.
10. Find the number of square yards of fabric needed to cover the base.
9 m
25 ft
4.4 in.12 cm
Practice Areas of Regular Polygons and Circles
NAME ______________________________________________ DATE ____________ PERIOD _____
11-311-3
Skills PracticeAreas of Irregular Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
11-411-4
© Glencoe/McGraw-Hill 631 Glencoe Geometry
Less
on
11-
4
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.
x
y
O
D(–2, –2)
G(4, 1)
H(2, –2)
E(–2, 4) F(2, 4)
x
y
O L(6, 0)
M(1, –3)
J(1, 4) K(5, 4)
x
y
O
Q(3, 5)
R(6, 7)P(0, 7)
T(3, 2)
U(0, 0) S(6, 0)x
y
O
D(8, 5)
E(8, 0)
C(3, 8)
B(3, 5)
A(0, 0)
30
15
8
8
7
3
5
12
20
© Glencoe/McGraw-Hill 632 Glencoe Geometry
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
LANDSCAPING For Exercises 7 and 8, use the following information.One of the displays at a botanical garden is a koi pond with a walkway around it.The figure shows the dimensions of the pond and the walkway.
7. Find the area of the pond to the nearest tenth.
8. Find the area of the walkway to the nearest tenth.
35 ft13 ft
15 ft7 ft
x
y
O S(2, 0)
Q(2, 6)
P(–2, 3)
T(–2, 1)
R(4, 3)
x
y
O
D(2, 5)
B(–1, 3)
A(–1, 0)
C(1, 4)E(4, 4)
F(4, 0)
13
13
20
30
23
7
9
38
22
22
20
20
Practice Areas of Irregular Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
11-411-4
Skills PracticeGeometric Probability
NAME ______________________________________________ DATE ____________ PERIOD _____
11-511-5
© Glencoe/McGraw-Hill 637 Glencoe Geometry
Less
on
11-
5
Find the probability that a point chosen at random lies in the shaded region.
1. 2.
Find the area of the indicated sector. Then find the probability of spinning thecolor indicated if the diameter of each spinner is 6 inches.
3. red
4. gold
5. blue
6. yellow
Find the area of the shaded region. Then find the probability that a point chosenat random is in the shaded region. Assume that all inscribed polygons are regular.
7. 8.
812
blue
blue
pink
red40!
40!30!
50!60!
70!70! red
yellow
yellow
gold
blue
bluered
gold60!
60!
60!100!
80!
© Glencoe/McGraw-Hill 638 Glencoe Geometry
Find the probability that a point chosen at random lies in the shaded region.
1. 2.
Find the area of the indicated sector. Then find the probability of spinning thecolor indicated if the diameter of the spinner is 9 meters.
3. red
4. blue
5. yellow
Find the area of the shaded region. Then find the probability that a point chosenat random is in the shaded region. Assume that all inscribed polygons are regular.
6. 7.
8. ARCHERY A target consists of four concentric rings. The radius of the center circle is 4 inches, and the circles are spaced 2 inches apart. Find the probability that an arrow shot at random by an inexperienced archer will land in a shaded region.
4 in.
2 in.
2 in.
2 in.
1711
blue
80!40!
100!85!
55!blue
red
redyellow
Practice Geometric Probability
NAME ______________________________________________ DATE ____________ PERIOD _____
11-511-5
© Glencoe/McGraw-Hill A2 Glencoe Geometry
Stu
dy
Gu
ide
and I
nte
rven
tion
Are
as o
f Par
alle
logr
ams
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-1
11-1
©G
lenc
oe/M
cGra
w-H
ill61
1G
lenc
oe G
eom
etry
Lesson 11-1
Are
as o
f Pa
ralle
log
ram
sA
par
alle
logr
am is
a q
uadr
ilate
ral w
ith
both
pai
rs o
fop
posi
te s
ides
par
alle
l.A
ny s
ide
of a
par
alle
logr
am c
an b
e ca
lled
a ba
se.E
ach
base
has
aco
rres
pond
ing
alti
tud
e,an
d th
e le
ngth
of
the
alti
tude
is t
he h
eigh
tof
the
par
alle
logr
am.
The
are
a of
a p
aral
lelo
gram
is t
he p
rodu
ct o
f th
e ba
se a
nd t
he h
eigh
t.
If a
para
llelo
gram
has
an
area
of A
squa
re u
nits
, A
rea
of a
Par
alle
logr
ama
base
of b
units
, and
a h
eigh
t of h
units
, th
en A
!bh
.
The
are
a of
par
alle
logr
am
AB
CD
is C
D"
AT.
Fin
d t
he
area
of
par
alle
logr
am E
FG
H.
A!
bhA
rea
of a
par
alle
logr
am
!30
(18)
b!
30, h
!18
!54
0M
ultip
ly.
The
are
a is
540
squ
are
met
ers.
Fin
d t
he
area
of
each
par
alle
logr
am.
1.2.
3.
288
ft2
288!
3"in
22.
56 c
m2
Fin
d t
he
area
of
each
sh
aded
reg
ion
.
4.W
XY
Zan
d A
BC
Dar
e 5.
All
angl
es a
re r
ight
6.
EF
GH
and
NO
PQ
are
rect
angl
es.
angl
es.
rect
angl
es;J
KL
Mis
asq
uare
.
452
cm2
51 f
t235
1 in
2
7.T
he a
rea
of a
par
alle
logr
am is
3.3
6 sq
uare
fee
t.T
he b
ase
is 2
.8 f
eet.
If t
he m
easu
res
ofth
e ba
se a
nd h
eigh
t ar
e ea
ch d
oubl
ed,f
ind
the
area
of
the
resu
ltin
g pa
ralle
logr
am.
13.4
4 ft
2
8.A
rec
tang
le is
4 m
eter
s lo
nger
tha
n it
is w
ide.
The
are
a of
the
rec
tang
le is
252
squ
are
met
ers.
Fin
d th
e le
ngth
.18
m
30 in
.
18 in
.EF G
H
JK
NO P
QL
M
9 in
.9
in.
9 in
.12
in.
12 ft
3 ft
3 ft 3 ft
8 ft
3 ft
2 ft
6 ft
32 c
m
16 c
m
12 c
m5
cm
WX Y
Z
AB
DC
1.6
cm
1.6
cm60
!
24 in
.
16 ft
18 ft
18 m
30 m
HG
FE
h
DT
C
BA
b
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill61
2G
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eom
etry
Para
llelo
gra
ms
on
th
e C
oo
rdin
ate
Plan
eTo
fin
d th
e ar
ea o
f a
quad
rila
tera
l on
the
coor
dina
te p
lane
,use
the
Slo
pe F
orm
ula,
the
Dis
tanc
e Fo
rmul
a,an
d pr
oper
ties
of
para
llelo
gram
s,re
ctan
gles
,squ
ares
,and
rho
mbi
.
Th
e ve
rtic
es o
f a
quad
rila
tera
l ar
e A
(#2,
2),
B(4
,2),
C(5
,#1)
,an
d D
(#1,
#1)
.
a.D
eter
min
e w
het
her
th
e qu
adri
late
ral
is a
squ
are
,a
rect
an
gle,
or a
pa
rall
elog
ram
.G
raph
the
qua
drila
tera
l.T
hen
dete
rmin
e th
e sl
ope
of e
ach
side
.
slop
e of
A !B!
!$ 4
2 ## (#
2 2)$
or 0
slop
e of
C !D!
!$#
#11#
#(#51)
$or
0
slop
e A !
D!!$ #2 2# #
(# (#1 1) )
$or
#3
slop
e B !
C!!
$# 51 ##42
$or
#3
Opp
osit
e si
des
have
the
sam
e sl
ope.
The
slo
pes
of c
onse
cuti
ve s
ides
are
not
neg
ativ
ere
cipr
ocal
s of
eac
h ot
her,
so c
onse
cuti
ve s
ides
are
not
per
pend
icul
ar.A
BC
Dis
apa
ralle
logr
am;i
t is
not
a r
ecta
ngle
or
a sq
uare
.
b.F
ind
th
e ar
ea o
f A
BC
D.
Fro
m t
he g
raph
,the
hei
ght
of t
he p
aral
lelo
gram
is 3
uni
ts a
nd A
B!
| 4 #
(#2)
| !6.
A!
bhA
rea
of a
par
alle
logr
am
!6(
3)b
!6,
h!
3
!18
uni
ts2
Mul
tiply
.
Giv
en t
he
coor
din
ates
of
the
vert
ices
of
a qu
adri
late
ral,
det
erm
ine
wh
eth
er t
he
quad
rila
tera
l is
a s
qua
re,a
rec
tan
gle,
or a
pa
rall
elog
ram
.Th
en f
ind
th
e ar
ea.
1.A
(#1,
2),B
(3,2
),C
(3,#
2),a
nd D
(#1,
#2)
squa
re;1
6 un
its2
2.R
(#1,
2),S
(5,0
),T
(4,#
3),a
nd U
(#2,
#1)
rect
angl
e;20
uni
ts2
3.C
(#2,
3),D
(3,3
),E
(5,0
),an
d F
(0,0
)pa
ralle
logr
am;1
5 un
its2
4.A
(#2,
#2)
,B(0
,2),
C(4
,0),
and
D(2
,#4)
squa
re;2
0 un
its2
5.M
(2,3
),N
(4,#
1),P
(#2,
#1)
,and
R(#
4,3)
para
llelo
gram
;24
units
2
6.D
(2,1
),E
(2,#
4),F
(#1,
#4)
,and
G(#
1,1)
rect
angl
e;15
uni
ts2
x
y
OD
C
BA
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Are
as o
f Par
alle
logr
ams
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-1
11-1
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 11-1)
© Glencoe/McGraw-Hill A3 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Are
a of
Par
alle
logr
ams
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-1
11-1
©G
lenc
oe/M
cGra
w-H
ill61
3G
lenc
oe G
eom
etry
Lesson 11-1
Fin
d t
he
per
imet
er a
nd
are
a of
eac
h p
aral
lelo
gram
.Rou
nd
to
the
nea
rest
ten
th i
fn
eces
sary
.
1.2.
100
cm,5
19.6
cm
219
ft,
19.1
ft2
3.4.
42 y
d,69
.3 y
d296
in.,
404.
5 in
2
5.6.
13.6
m,1
1.6
m2
55 k
m,1
66.5
km
2
Fin
d t
he
area
of
each
fig
ure
.
7.8.
14 u
nits
258
uni
ts2
CO
OR
DIN
ATE
GEO
MET
RYG
iven
th
e co
ord
inat
es o
f th
e ve
rtic
es o
f a
quad
rila
tera
l,d
eter
min
e w
het
her
it
is a
squ
are
,a r
ecta
ngl
e,or
a p
ara
llel
ogra
m.T
hen
fin
d t
he
area
of
the
quad
rila
tera
l.
9.A
(#4,
2),B
(#1,
2),C
(#1,
#1)
,10
.P(#
3,3)
,Q(1
,3),
R(1
,#3)
,D
(#4,
#1)
S(#
3,#
3)sq
uare
,9 u
nits
2re
ctan
gle,
24 u
nits
2
11.D
(#5,
1),E
(7,1
),F
(4,#
4),
12.R
(2,3
),S
(4,1
0),T
(12,
10),
G(#
8,#
4)U
(10,
3)pa
ralle
logr
am,6
0 un
its2
para
llelo
gram
,56
units
2
8 22
2222
26
33
4
66
1 1
1
11
2 22 2
1
18.5
km
9 km
3.4
m
26 in
.
22 in
.
45!
14 y
d
7 yd
45!
5.5
ft
4 ft 60
!
20 c
m
30 c
m60
!
©G
lenc
oe/M
cGra
w-H
ill61
4G
lenc
oe G
eom
etry
Fin
d t
he
per
imet
er a
nd
are
a of
eac
h p
aral
lelo
gram
.Rou
nd
to
the
nea
rest
ten
th i
fn
eces
sary
.
1.2.
3.
32 m
,47.
6 m
236
cm
,56.
6 cm
234
.1 in
.,50
in2
Fin
d t
he
area
of
each
fig
ure
.
4.5.
44 u
nits
265
uni
ts2
CO
OR
DIN
ATE
GEO
MET
RYG
iven
th
e co
ord
inat
es o
f th
e ve
rtic
es o
f a
quad
rila
tera
l,d
eter
min
e w
het
her
it
is a
squ
are
,a r
ecta
ngl
e,or
a p
ara
llel
ogra
m.T
hen
fin
d t
he
area
of
the
quad
rila
tera
l.
6.C
(#4,
#1)
,D(#
4,2)
,F(1
,2),
G(1
,#1)
7.W
(2,2
),X
(1,#
2),Y
(#2,
#2)
,Z(#
1,2)
rect
angl
e,15
uni
ts2
para
llelo
gram
,12
units
2
8.M
(0,4
),N
(4,6
),O
(6,2
),P
(2,0
)9.
P(#
5,2)
,Q(4
,2),
R(5
,5),
S(#
4,5)
squa
re,2
0 un
its2
para
llelo
gram
,27
units
2
FRA
MIN
GF
or E
xerc
ises
10–
12,u
se t
he
foll
owin
g in
form
atio
n.
A r
ecta
ngul
ar p
oste
r m
easu
res
42 in
ches
by
26 in
ches
.A f
ram
e sh
op f
itte
d th
e po
ster
wit
h a
half
-inc
h m
at b
orde
r.
10.F
ind
the
area
of
the
post
er.
1092
in2
11.F
ind
the
area
of
the
mat
bor
der.
69 in
2
12.S
uppo
se t
he w
all i
s m
arke
d w
here
the
pos
ter
will
han
g.T
he m
arke
d ar
ea in
clud
es a
nad
diti
onal
12-
inch
spa
ce a
roun
d th
e po
ster
and
fra
me.
Fin
d th
e to
tal w
all a
rea
that
has
been
mar
ked
for
the
post
er.
3417
in2
773
34
31
33
3 3
2
2
22
8
92
2
2
22
2
1
1
4 4
4
10 in
.
45!
10 c
m
8 cm 45
!
5 m
11 m
60!
Pra
ctic
e (A
vera
ge)
Are
a of
Par
alle
logr
ams
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-1
11-1
Answers (Lesson 11-1)
© Glencoe/McGraw-Hill A4 Glencoe Geometry
Rea
din
g t
o L
earn
Math
emati
csA
reas
of P
aral
lelo
gram
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-1
11-1
©G
lenc
oe/M
cGra
w-H
ill61
5G
lenc
oe G
eom
etry
Lesson 11-1
Pre-
Act
ivit
yH
ow i
s ar
ea r
elat
ed t
o ga
rden
des
ign
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 11
-1 a
t th
e to
p of
pag
e 59
5 in
you
r te
xtbo
ok.
How
cou
ld y
ou d
escr
ibe
the
patt
ern
you
see
in t
he p
ictu
re o
f th
e ga
rden
so
that
som
eone
who
doe
sn’t
have
the
pic
ture
will
kno
w w
hat
it lo
oks
like?
Sam
ple
answ
er:T
here
are
squ
ares
of
gran
ite a
nd s
quar
es o
fm
oss
of t
he s
ame
size
pla
ced
in a
che
cker
boar
d de
sign
.
Rea
din
g t
he
Less
on
1.W
hich
exp
ress
ion
give
s th
e ar
ea o
f th
e pa
ralle
logr
am?
(Hin
t:T
here
can
be
mor
e th
an o
ne c
orre
ct r
espo
nse.
)B
,D,E
,GA
.ab
B.c
bC
.ed
D.a
fE
.ce
F.cd
G.d
fH
.bf
I.cf
2.R
efer
to
the
figu
re.D
eter
min
e w
heth
er e
ach
stat
emen
t
is t
rue
or f
alse
.If
the
stat
emen
t is
fal
se,e
xpla
in w
hy.
a.A!
B!is
an
alti
tude
of
the
para
llelo
gram
.Fa
lse;
A"B"
is n
otpe
rpen
dicu
lar
to a
ny s
ide
of t
he p
aral
lelo
gram
.
b.C!
D!is
a b
ase
of p
aral
lelo
gram
AB
CD
.tr
ue
c.T
he p
erim
eter
of A
BC
Dis
(2x
%2y
) un
its2
.Fa
lse;
peri
met
er is
mea
sure
d in
linea
r un
its,n
ot s
quar
e un
its.T
he p
erim
eter
is (
2x"
2y)
units
.d.
BE
!C
Ftr
ue
e.B
E!
xFa
lse;
B"E"
is o
ppos
ite t
he 3
0°an
gle
in a
30°
-60°
-90°
tria
ngle
,so
BE
#$1 2$ x
or $x 2$ .
f.T
he a
rea
of A
BC
Dis
2xy
unit
s2.
Fals
e;si
nce
BE
#$x 2$ ,
the
area
of
AB
CD
is $x 2y $
units
2 .
Hel
pin
g Y
ou
Rem
emb
er
3.A
goo
d w
ay t
o re
mem
ber
a ne
w f
orm
ula
in g
eom
etry
is t
o re
late
it t
o a
form
ula
you
alre
ady
know
.How
can
you
use
the
for
mul
a fo
r th
e ar
ea o
f a
rect
angl
e to
hel
p yo
ure
mem
ber
the
form
ula
for
the
area
of
a pa
ralle
logr
am?
Sam
ple
answ
er:T
o fin
d th
e ar
ea o
f a
rect
angl
e,yo
u m
ultip
ly t
he le
ngth
sof
tw
o se
gmen
ts t
hat
are
perp
endi
cula
r to
eac
h ot
her.
To f
ind
the
area
of
a pa
ralle
logr
am,y
ou d
o th
e sa
me
thin
g,bu
t th
e he
ight
is n
ot n
eces
sari
lyon
e of
the
sid
es.
"3!
$2
x
y
d
AE
DFC
B
30!
30!
ad
fe
bc
©G
lenc
oe/M
cGra
w-H
ill61
6G
lenc
oe G
eom
etry
Are
a of
a P
aral
lelo
gram
You
can
prov
e so
me
inte
rest
ing
resu
lts
usin
g th
e fo
rmul
a yo
u ha
ve p
rove
d fo
r th
e ar
ea o
f a
para
llelo
gram
by
draw
ing
auxi
liary
line
s to
for
m c
ongr
uent
reg
ions
.Con
side
r th
e to
ppa
ralle
logr
am s
how
n at
the
rig
ht.I
n th
e fi
gure
,dis
the
le
ngth
of
the
diag
onal
B !D !
,and
kis
the
leng
th o
f th
epe
rpen
dicu
lar
segm
ent
from
Ato
B !D !
.Now
con
side
r th
e se
cond
fig
ure,
whi
ch s
how
s th
e sa
me
para
llelo
gram
wit
h a
num
ber
of a
uxili
ary
perp
endi
cula
rs a
dded
.Use
wha
t yo
u kn
ow a
bout
per
pend
icul
ar li
nes,
para
llel l
ines
,and
co
ngru
ent
tria
ngle
s to
ans
wer
the
fol
low
ing.
1.W
hat
kind
of
figu
re is
DB
HG
?
rect
angl
e
2.If
you
mov
ed !
AF
Bto
the
low
er-l
eft
end
of f
igur
e D
BH
G,w
ould
it f
it p
erfe
ctly
on
top
of !
DG
C?
Exp
lain
yo
ur a
nsw
er.
Yes;
!A
FB#
!C
ED
(by
HA
) an
d !
CE
D#
!D
GC
(s
ince
D "C "
is a
dia
gona
l of
rect
angl
e D
EC
D).
So
!A
FB#
!D
GC
.
3.W
hich
tw
o tr
iang
ular
pie
ces
of "
AB
CD
are
cong
ruen
t to
!C
BH
?
!D
AF
and
!B
CE
4.T
he a
rea
of "
AB
CD
is t
he s
ame
as t
hat
of f
igur
e D
BH
G,
sinc
e th
e pi
eces
of "
AB
CD
can
be r
earr
ange
d to
for
m
DB
HG
.Exp
ress
the
are
a of
"A
BC
Din
ter
ms
of t
he
mea
sure
men
ts k
and
d.
Are
a of
"A
BC
D#
dk
AB
AB
H
DC
DC
k k k
FE
G
d
d
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-1
11-1
Answers (Lesson 11-1)
© Glencoe/McGraw-Hill A5 Glencoe Geometry
An
swer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Are
as o
f Tri
angl
es,T
rape
zoid
s,an
d R
hom
bi
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-2
11-2
©G
lenc
oe/M
cGra
w-H
ill61
7G
lenc
oe G
eom
etry
Lesson 11-2
Are
as o
f Tr
ian
gle
sT
he a
rea
of a
tri
angl
e is
hal
f th
e ar
ea o
f a
rect
angl
e w
ith
the
sam
eba
se a
nd h
eigh
t as
the
tri
angl
e.
If a
tria
ngle
has
an
area
of A
squa
re u
nits
, a b
ase
of b
units
,
and
a co
rres
pond
ing
heig
ht o
f hun
its, t
hen
A!
$1 2$ bh.
Fin
d t
he
area
of
the
tria
ngl
e.
A!
$1 2$ bh
Are
a of
a tr
iang
le
!$1 2$ (
24)(
28)
b!
24, h
!28
!33
6M
ultip
ly.
The
are
a is
336
squ
are
met
ers.
Fin
d t
he
area
of
each
fig
ure
.
1.2.
498
units
216
40 u
nits
2
3.4.
25 u
nits
233
2.6
units
2
5.6.
1017
uni
ts2
672
units
2
7.T
he a
rea
of a
tri
angl
e is
72
squa
re in
ches
.If
the
heig
ht is
8 in
ches
,fin
d th
e le
ngth
of
the
base
.18
in.
8.A
rig
ht t
rian
gle
has
a pe
rim
eter
of
36 m
eter
s,a
hypo
tenu
se o
f 15
met
ers,
and
a le
g of
9
met
ers.
Fin
d th
e ar
ea o
f th
e tr
iang
le.
54 m
2
2424
18 10
21
15 60
54
24
60!
10
20
20
26
56
21
2016
33
28 m
24 m
h
ZY
X
b
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill61
8G
lenc
oe G
eom
etry
Are
as o
f Tr
apez
oid
s an
d R
ho
mb
iT
he a
rea
of a
tra
pezo
id is
the
pro
duct
of
half
the
heig
ht a
nd t
he s
um o
f th
e le
ngth
s of
the
bas
es.T
he a
rea
of a
rho
mbu
s is
hal
f th
e pr
oduc
t of
the
diag
onal
s.
If a
trap
ezoi
d ha
s an
are
a of
Asq
uare
uni
ts, b
ases
of
If a
rhom
bus
has
an a
rea
of A
squa
re u
nits
and
b 1an
d b 2
units
, and
a h
eigh
t of h
units
, the
ndi
agon
als
of d
1an
d d 2
units
, the
n
A!
$1 2$ h(b
1%
b 2).
A!
$1 2$ d1d
2.
Fin
d t
he
area
of
the
trap
ezoi
d.
A!
$1 2$ h(b
1%
b 2)
Are
a of
a tr
apez
oid
!$1 2$ (
15)(
18 %
40)
h!
15, b
1!
18, b
2!
40
!43
5S
impl
ify.
The
are
a is
435
squ
are
met
ers.
Fin
d t
he
area
of
each
qu
adri
late
ral
give
n t
he
coor
din
ates
of
the
vert
ices
.
1.2.
400
units
272
!3"
units
2
3.4.
512
units
240
0 un
its2
5.6.
338
units
250
4 un
its2
7.T
he a
rea
of a
tra
pezo
id is
144
squ
are
inch
es.I
f th
e he
ight
is 1
2 in
ches
,fin
d th
e le
ngth
of
the
med
ian.
12 in
.
8.A
rho
mbu
s ha
s a
peri
met
er o
f 80
met
ers
and
the
leng
th o
f on
e di
agon
al is
24
met
ers.
Fin
d th
e ar
ea o
f th
e rh
ombu
s.38
4 m
2
28
1224
13 1313
13
18
16
32
1632
1260
!
10 10
2020
40 m18
m
15 m
d 2d 1
h
b 2b 1
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Are
as o
f Tri
angl
es,T
rape
zoid
s,an
d R
hom
bi
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-2
11-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 11-2)
© Glencoe/McGraw-Hill A6 Glencoe Geometry
Skil
ls P
ract
ice
Are
as o
f Tri
angl
es,T
rape
zoid
s,an
d R
hom
bi
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-2
11-2
©G
lenc
oe/M
cGra
w-H
ill61
9G
lenc
oe G
eom
etry
Lesson 11-2
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.
22.5
ft2
425
in2
896
cm2
Fin
d t
he
area
of
each
qu
adri
late
ral
give
n t
he
coor
din
ates
of
the
vert
ices
.
4.tr
apez
oid
WX
YZ
5.rh
ombu
s H
IJK
W(#
5,3)
,X(3
,3),
Y(6
,#3)
,Z(#
8,#
3)H
(4,#
3),I
(2,#
7),J
(0,#
3),K
(2,1
)66
uni
ts2
16 u
nits
2
Fin
d t
he
mis
sin
g m
easu
re f
or e
ach
fig
ure
.
6.T
rape
zoid
RS
TU
has
an a
rea
of
7.T
rape
zoid
JK
LM
has
an a
rea
of
935
squa
re c
enti
met
ers.
Fin
d th
e 7.
5 sq
uare
inch
es.F
ind
ML
.he
ight
of R
ST
U.
22 c
m2.
5 in
.
8.T
rian
gle
AB
Cha
s an
are
a of
9.
Rho
mbu
s E
FG
Hha
s an
are
a of
10
50 s
quar
e m
eter
s.F
ind
the
750
squa
re f
eet.
If E
Gis
50
feet
,he
ight
of !
AB
C.
find
FH
.
35 m
30 f
t
HE
FG
AC
B
60 m
ML
JK
5 in
.
2 in
.
55 c
mR
U
TS
30 c
m
34 c
m28
cm
21 c
m
40 c
m
22 in
.
12 in
.25
in.
4 ft
3.5
ft6
ft
©G
lenc
oe/M
cGra
w-H
ill62
0G
lenc
oe G
eom
etry
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
7.6
m2
26.5
cm
2
3.
767
ft2
Fin
d t
he
area
of
each
qu
adri
late
ral
give
n t
he
coor
din
ates
of
the
vert
ices
.
4.tr
apez
oid
AB
CD
5.rh
ombu
s L
MN
OA
(#7,
1),B
(#4,
4),C
(#4,
#6)
,L
(6,8
),M
(14,
4),N
(6,0
),D
(#7,
#3)
O(#
2,4)
21 u
nits
264
uni
ts2
Fin
d t
he
mis
sin
g m
easu
re f
or e
ach
fig
ure
.
6.T
rape
zoid
WX
YZ
has
an a
rea
of
7.T
rian
gle
PR
Sha
s an
are
a of
13
.75
squa
re m
eter
s.F
ind
WX
.68
squ
are
yard
s.If
the
hei
ght
of !
PR
Sis
8 y
ards
,fin
d th
e ba
se.
7.5
m17
yd
DES
IGN
For
Exe
rcis
es 8
an
d 9
,use
th
e fo
llow
ing
info
rmat
ion
.M
r.H
agar
ty u
sed
16 c
ongr
uent
rho
mbi
-sha
ped
tile
s to
des
ign
the
mid
sect
ion
of t
he b
acks
plas
h ar
ea a
bove
a k
itch
en s
ink.
The
leng
th
of t
he d
esig
n is
27
inch
es a
nd t
he t
otal
are
a is
108
squ
are
inch
es.
8.F
ind
the
area
of
one
rhom
bus.
6$3 4$
in2
9.F
ind
the
leng
th o
f ea
ch d
iago
nal.
4$1 2$
in.,
3 in
.
PS
R
ZY
WX
3.5
m
2.5
m
37 ft
22 ft
26 ft
10 c
m
3 cm
6 cm
3.5
cm
4 m2.
6 m
1.5
m
3.2 m
Pra
ctic
e (A
vera
ge)
Are
as o
f Tri
angl
es,T
rape
zoid
s,an
d R
hom
bi
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-2
11-2
Answers (Lesson 11-2)
© Glencoe/McGraw-Hill A7 Glencoe Geometry
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csA
reas
of T
rian
gles
,Tra
pezo
ids,
and
Rho
mbi
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-2
11-2
©G
lenc
oe/M
cGra
w-H
ill62
1G
lenc
oe G
eom
etry
Lesson 11-2
Pre-
Act
ivit
yH
ow i
s th
e ar
ea o
f a
tria
ngl
e re
late
d t
o be
ach
um
brel
las?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 11
-2 a
t th
e to
p of
pag
e 60
1 in
you
r te
xtbo
ok.
Cla
ssif
y th
e po
lygo
ns in
the
pan
els
of t
he b
each
um
brel
la.
Isos
cele
s tr
iang
les
and
isos
cele
s tr
apez
oids
Rea
din
g t
he
Less
on
1.M
atch
eac
h ar
ea f
orm
ula
from
the
fir
st c
olum
n w
ith
the
corr
espo
ndin
g po
lygo
n in
the
seco
nd c
olum
n.
a.A
!!w
vii.
tria
ngle
b.A
!$1 2$ d
1d2
ivii
.par
alle
logr
am
c.A
!s2
vii
i.tr
apez
oid
d.A
!$1 2$ h
(b1
%b 2
)iii
iv.
rhom
bus
e.A
!$1 2$ b
hi
v.sq
uare
f.A
!bh
iivi
.rec
tang
le
2.D
eter
min
e w
heth
er e
ach
stat
emen
t is
alw
ays,
som
etim
es,o
r ne
ver
true
.In
each
cas
e,ex
plai
n yo
ur r
easo
ning
.Fo
r ex
plan
atio
ns,s
ampl
e an
swer
s ar
e gi
ven.
a.T
he a
rea
of a
squ
are
is h
alf
the
prod
uct
of it
s di
agon
als.
Alw
ays;
a sq
uare
is a
rhom
bus,
so y
ou c
an u
se t
he r
hom
bus
form
ula.
b.T
he a
rea
of a
tri
angl
e is
hal
f th
e pr
oduc
t of
tw
o of
its
side
s.S
omet
imes
;thi
s is
true
onl
y fo
r a
righ
t tr
iang
le.
c.Yo
u ca
n fin
d th
e ar
ea o
f a r
ecta
ngle
by
mul
tipl
ying
bas
e ti
mes
hei
ght.
Alw
ays;
are
ctan
gle
is a
par
alle
logr
am,s
o yo
u ca
n us
e th
e pa
ralle
logr
am fo
rmul
a.If
the
leng
th o
f a r
ecta
ngle
is u
sed
as th
e ba
se,t
hen
the
wid
th is
the
heig
ht.
d.Yo
u ca
n fi
nd t
he a
rea
of a
rec
tang
le b
y m
ulti
plyi
ng t
he le
ngth
s of
any
tw
o of
its
side
s.S
omet
imes
;thi
s is
tru
e on
ly fo
r a
squa
re.O
ther
wis
e,yo
u m
ust
use
two
cons
ecut
ive
side
s,no
t an
y tw
o si
des.
e.T
he a
rea
of a
tra
pezo
id is
the
pro
duct
of
its
heig
ht a
nd t
he s
um o
f th
e ba
ses.
Nev
er;
the
area
is o
ne-h
alf
the
prod
uct
of it
s he
ight
and
the
sum
of
the
base
s.
f.T
he s
quar
e of
the
leng
th o
f a
side
of
a sq
uare
is e
qual
to
half
the
pro
duct
of
its
diag
onal
s.A
lway
s;a
squa
re is
a r
hom
bus,
so t
he fo
rmul
as fo
r a
squa
rean
d a
rhom
bus
mus
t gi
ve t
he s
ame
answ
er w
hene
ver
the
rhom
bus
is a
squa
re.
Hel
pin
g Y
ou
Rem
emb
er3.
A g
ood
way
to
rem
embe
r a
new
geo
met
ric
form
ula
is t
o st
ate
it in
wor
ds.W
rite
a s
hort
sent
ence
tha
t te
lls h
ow t
o fi
nd t
he a
rea
of a
tra
pezo
id in
a w
ay t
hat
is e
asy
to r
emem
ber.
Sam
ple
answ
er:A
vera
ge t
he le
ngth
s of
the
bas
es a
nd m
ultip
ly b
y th
ehe
ight
.
©G
lenc
oe/M
cGra
w-H
ill62
2G
lenc
oe G
eom
etry
Are
as o
f Sim
ilar T
rian
gles
You
have
lear
ned
that
if t
wo
tria
ngle
s ar
e si
mila
r,th
e ra
tio
of t
he le
ngth
s of
cor
resp
ondi
ngal
titu
des
is e
qual
to
the
rati
o of
the
leng
ths
of a
pai
r of
cor
resp
ondi
ng s
ides
.How
ever
,the
reis
a d
iffe
rent
rel
atio
nshi
p be
twee
n th
e ar
eas
of t
he t
wo
tria
ngle
s.
Th
eore
mIf
tw
o tr
iang
les
are
sim
ilar,
the
rati
o of
the
ir a
reas
is t
he s
quar
e of
the
rat
io o
fth
e le
ngth
s of
a p
air
of c
orre
spon
ding
sid
es.
Tri
angl
e II
is k
tim
es la
rger
tha
n T
rian
gle
I.T
hus,
its
base
is k
tim
es
as la
rge
as t
hat
of T
rian
gle
I an
d it
s he
ight
is k
tim
es a
s la
rge
as t
hat
ofT
rian
gle
I.
$s si id de eo of f! !I II
$!
$k bb $or
$k 1$
$a ar re ea ao of f! !
I II$
!or
$k 12 $
Sol
ve.
1.!
DE
F#
!G
HJ,
HJ
!16
,and
EF
!8.
2.In
the
fig
ure
belo
w,P!
Q!|| B!
C!.T
he a
rea
ofT
he a
rea
of !
GH
Jis
40.
Fin
d th
e ar
ea
!A
BC
is 7
2.F
ind
the
area
of !
AP
Q.
8of
!D
EF
.10
3.T
wo
sim
ilar
tria
ngle
s ha
ve a
reas
of
16 a
nd 3
6.T
he le
ngth
of
a si
de o
f th
e sm
alle
rtr
iang
le is
10
feet
.Fin
d th
e le
ngth
of
the
corr
espo
ndin
g si
de o
f th
e la
rger
tri
angl
e.
15 f
t
4.F
ind
the
rati
o of
the
are
as o
f tw
o si
mila
r tr
iang
les
if t
he le
ngth
s of
tw
o co
rres
pond
ing
side
s of
the
tri
angl
es a
re 3
cen
tim
eter
s an
d 5
cent
imet
ers.
$ 29 5$
BC
QP
8
43
6
A
HJ
GE
F
D
Tri
angl
e II
area
!II
!$1 2$ (
kb)(
kh)
!$1 2$ k
2 bh
Tri
angl
e I
area
!I
!$1 2$ b
h$1 2$ k
2 bh
$$
$1 2$ bh
kh
kb
h
b
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-2
11-2
Answers (Lesson 11-2)
© Glencoe/McGraw-Hill A8 Glencoe Geometry
Stu
dy
Gu
ide
and I
nte
rven
tion
Are
as o
f Reg
ular
Pol
ygon
s an
d C
ircl
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-3
11-3
©G
lenc
oe/M
cGra
w-H
ill62
3G
lenc
oe G
eom
etry
Lesson 11-3
Are
as o
f R
egu
lar
Poly
go
ns
In a
reg
ular
pol
ygon
,the
seg
men
t
draw
n fr
om t
he c
ente
r of
the
pol
ygon
per
pend
icul
ar t
o th
e op
posi
te s
ide
is c
alle
d th
e ap
oth
em.I
n th
e fi
gure
at
the
righ
t,A !
P!is
the
apo
them
and
A !
R!is
the
rad
ius
of t
he c
ircu
msc
ribe
d ci
rcle
.
If a
regu
lar
poly
gon
has
an a
rea
of A
squa
re u
nits
,
Are
a of
a R
egul
ar P
olyg
ona
perim
eter
of P
units
, and
an
apot
hem
of a
units
,
then
A!
$1 2$ Pa.
U
V
R
A PS
T
Ver
ify
the
form
ula
A!
$1 2$ Pa
for
the
regu
lar
pen
tago
n a
bove
.
For
!R
AS
,the
are
a is
A!
$1 2$ bh
!$1 2$ (
RS
)(A
P).
So t
he a
rea
of t
he
pent
agon
is A
!5 $$1 2$ %(R
S)(
AP
).Su
bsti
tuti
ng
Pfo
r 5R
San
d su
bsti
tuti
ng a
for
AP
,the
n
A!
$1 2$ Pa.
Fin
d t
he
area
of
regu
lar
pen
tago
n R
ST
UV
abov
e if
its
per
imet
eris
60
cen
tim
eter
s.F
irst
fin
d th
e ap
othe
m.
The
mea
sure
of
cent
ral a
ngle
RA
Sis
$36 50 $or
72
.The
refo
re m
#R
AP
!36
.The
per
imet
eris
60,
so R
S!
12 a
nd R
P!
6.
tan
#R
AP
!$R A
PP $
tan
36°
!$ A6 P$
AP
!$ ta
n6 36°
$
&8.
26
So A
!$1 2$ P
a!
$1 2$ 60(
8.26
) or
247
.7.
The
are
a is
abo
ut 2
48 s
quar
e ce
ntim
eter
s.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
area
of
each
reg
ula
r p
olyg
on.R
oun
d t
o th
e n
eare
st t
enth
.
1.2.
3.
84.9
m2
172.
0 in
222
5 in
2
4.5.
6.
259.
8 cm
248
2.8
in2
204.
4 m
210.9
m 7.5
m10
in.
5"'3
cm
15 in
.10
in.
14 m
©G
lenc
oe/M
cGra
w-H
ill62
4G
lenc
oe G
eom
etry
Are
as o
f C
ircl
esA
s th
e nu
mbe
r of
sid
es o
f a
regu
lar
poly
gon
incr
ease
s,th
e po
lygo
n ge
tscl
oser
and
clo
ser
to a
cir
cle
and
the
area
of
the
poly
gon
gets
clo
ser
to t
he a
rea
of a
cir
cle.
Are
a of
a C
ircl
eIf
a ci
rcle
has
an
area
of A
squa
re u
nits
an
d a
radi
us o
f run
its, t
hen
A!
&r2
.
Cir
cle
Qis
in
scri
bed
in
squ
are
RS
TU
.Fin
d t
he
area
of
the
shad
ed r
egio
n.
A s
ide
of t
he s
quar
e is
40
met
ers,
so t
he r
adiu
s of
the
cir
cle
is 2
0 m
eter
s.
The
sha
ded
area
is
Are
a of
RS
TU
#A
rea
of c
ircl
e Q
!40
2#
&r2
!16
00 #
400&
&16
00 #
1256
.6!
343.
4 m
2
Fin
d t
he
area
of
each
sh
aded
reg
ion
.Ass
um
e th
at a
ll p
olyg
ons
are
regu
lar.
Rou
nd
to t
he
nea
rest
ten
th.
1.2.
3.
37.7
in2
3.4
m2
100.
5 m
2
4.5.
6.
37.7
in2
164.
4 in
230
.9 m
2
12 m
12 m
4 in
.
16 m
4 m
2 in
.2
in.
Q
RS T
U40
m
40 m
Or
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Are
as o
f Reg
ular
Pol
ygon
s an
d C
ircl
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-3
11-3
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 11-3)
© Glencoe/McGraw-Hill A9 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Are
as o
f Reg
ular
Pol
ygon
s an
d C
ircl
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-3
11-3
©G
lenc
oe/M
cGra
w-H
ill62
5G
lenc
oe G
eom
etry
Lesson 11-3
Fin
d t
he
area
of
each
reg
ula
r p
olyg
on.R
oun
d t
o th
e n
eare
st t
enth
.
1.a
pent
agon
wit
h a
peri
met
er o
f 45
fee
t13
9.4
ft2
2.a
hexa
gon
wit
h a
side
leng
th o
f 4
inch
es41
.6 in
2
3.a
nona
gon
wit
h a
side
leng
th o
f 8
met
ers
395.
6 m
2
4.a
tria
ngle
wit
h a
peri
met
er o
f 54
cen
tim
eter
s14
0.3
cm2
Fin
d t
he
area
of
each
cir
cle.
Rou
nd
to
the
nea
rest
ten
th.
5.a
circ
le w
ith
a ra
dius
of
6 ya
rds
113.
1 yd
2
6.a
circ
le w
ith
a di
amet
er o
f 18
mill
imet
ers
254.
5 m
m2
Fin
d t
he
area
of
each
sh
aded
reg
ion
.Ass
um
e th
at a
ll p
olyg
ons
are
regu
lar.
Rou
nd
to t
he
nea
rest
ten
th.
7.8.
16.6
in2
19.4
m2
9.10
.
32.9
ft2
21.5
cm
2
5 cm
4 ft
8 m
4 m
3 in
.
©G
lenc
oe/M
cGra
w-H
ill62
6G
lenc
oe G
eom
etry
Fin
d t
he
area
of
each
reg
ula
r p
olyg
on.R
oun
d t
o th
e n
eare
st t
enth
.
1.a
nona
gon
wit
h a
peri
met
er o
f 11
7 m
illim
eter
s10
44.7
mm
2
2.an
oct
agon
wit
h a
peri
met
er o
f 96
yar
ds69
5.3
yd2
Fin
d t
he
area
of
each
cir
cle.
Rou
nd
to
the
nea
rest
ten
th.
3.a
circ
le w
ith
a di
amet
er o
f 26
fee
t53
0.9
ft2
4.a
circ
le w
ith
a ci
rcum
fere
nce
of 8
8 ki
lom
eter
s61
6.2
km2
Fin
d t
he
area
of
each
sh
aded
reg
ion
.Ass
um
e th
at a
ll p
olyg
ons
are
regu
lar.
Rou
nd
to t
he
nea
rest
ten
th.
5.6.
164.
4 cm
235
.7 in
2
7.8.
339.
7 ft
216
6.4
m2
DIS
PLA
YS
For
Exe
rcis
es 9
an
d 1
0,u
se t
he
foll
owin
g in
form
atio
n.
A d
ispl
ay c
ase
in a
jew
elry
sto
re h
as a
bas
e in
the
sha
pe o
f a
regu
lar
octa
gon.
The
leng
th o
fea
ch s
ide
of t
he b
ase
is 1
0 in
ches
.The
ow
ners
of
the
stor
e pl
an t
o co
ver
the
base
in b
lack
velv
et.
9.F
ind
the
area
of
the
base
of
the
disp
lay
case
.ab
out
482.
8 in
2
10.F
ind
the
num
ber
of s
quar
e ya
rds
of f
abri
c ne
eded
to
cove
r th
e ba
se.
abou
t 0.
37 y
d2
9 m
25 ft
4.4
in.
12 c
mPra
ctic
e (A
vera
ge)
Are
as o
f Reg
ular
Pol
ygon
s an
d C
ircl
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-3
11-3
Answers (Lesson 11-3)
© Glencoe/McGraw-Hill A10 Glencoe Geometry
Rea
din
g t
o L
earn
Math
emati
csA
reas
of R
egul
ar P
olyg
ons
and
Cir
cles
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-3
11-3
©G
lenc
oe/M
cGra
w-H
ill62
7G
lenc
oe G
eom
etry
Lesson 11-3
Pre-
Act
ivit
yH
ow c
an y
ou f
ind
th
e ar
ea o
f a
pol
ygon
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 11
-3 a
t th
e to
p of
pag
e 61
0 in
you
r te
xtbo
ok.
How
can
you
fin
d th
e ar
ea o
f a
regu
lar
hexa
gon
wit
hout
a n
ew a
rea
form
ula?
Sam
ple
answ
er:D
ivid
e th
e he
xago
n in
to s
ix c
ongr
uent
equi
late
ral t
rian
gles
.Use
pro
pert
ies
of t
he 3
0°-6
0°-9
0°tr
iang
leto
fin
d th
e ar
ea o
f on
e of
the
se t
rian
gles
and
mul
tiply
the
resu
lt by
6.
Rea
din
g t
he
Less
on
1.A
BC
DE
Fan
d R
ST
UV
are
regu
lar
poly
gons
.N
ame
each
of
the
follo
win
g in
one
of
the
figu
res.
a.a
circ
umsc
ribe
d po
lygo
nhe
xago
n A
BC
DE
Fb.
an in
scri
bed
poly
gon
pent
agon
RS
TUV
c.an
apo
them
of
a re
gula
r he
xago
nG"
H"d.
an is
osce
les
tria
ngle
!P
RS
or !
GA
Be.
a 30
°-60
°-90
°tr
iang
le!
GA
Hor
!G
BH
f.a
cent
ral a
ngle
wit
h a
mea
sure
of
72#
RP
S
2.R
efer
to
the
figu
res
in E
xerc
ise
1.M
atch
eac
h it
em in
the
fir
st c
olum
n w
ith
anex
pres
sion
in t
he s
econ
d co
lum
n.
a.pe
rim
eter
of A
BC
DE
Fv
i.&
(PS
)2
b.ci
rcum
fere
nce
of c
ircl
e G
viii
ii.2
&(P
R)
c.pe
rim
eter
of R
ST
UV
vii
iii.
$5 2$ (R
S)(
PQ
)
d.ar
ea o
f ci
rcle
Gvi
iv.
3(A
B)(
HG
)
e.ar
ea o
f RS
TU
Viii
v.6(
CD
)
f.ar
ea o
f AB
CD
EF
ivvi
.&(G
H)2
g.ar
ea o
f ci
rcle
Pi
vii.
5(U
V)
h.
circ
umfe
renc
e of
cir
cle
Pii
viii
.2&
(GH
)
3.E
xpla
in in
you
r ow
n w
ords
how
to
find
the
are
a of
a c
ircl
e if
you
kno
w t
heci
rcum
fere
nce.
Sam
ple
answ
er:D
ivid
e th
e ci
rcum
fere
nce
by 2
%to
fin
d th
era
dius
.The
n sq
uare
the
rad
ius
and
mul
tiply
by
%to
fin
d th
e ar
ea.
Hel
pin
g Y
ou
Rem
emb
er
4.A
goo
d w
ay t
o re
mem
ber
som
ethi
ng is
to
expl
ain
it t
o so
meo
ne e
lse.
Supp
ose
your
clas
smat
e Jo
elle
is h
avin
g tr
oubl
e re
mem
beri
ng w
hich
for
mul
a is
for
cir
cum
fere
nce
and
whi
ch is
for
are
a.H
ow c
an y
ou h
elp
her?
Sam
ple
answ
er:C
ircu
mfe
renc
e is
mea
sure
d in
line
ar u
nits
,whi
le a
rea
is m
easu
red
in s
quar
e un
its,s
o th
efo
rmul
a co
ntai
ning
r2
mus
t be
the
one
for
area
.
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R
PSB
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w-H
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8G
lenc
oe G
eom
etry
Are
as o
f Ins
crib
ed P
olyg
ons
A p
rotr
acto
r ca
n b
e u
sed
to
insc
ribe
a r
egu
lar
pol
ygon
in
a c
ircl
e.F
ollo
w t
he
step
s be
low
to
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ribe
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egu
lar
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agon
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.
Ste
p 1
Fin
d th
e de
gree
mea
sure
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each
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the
nine
con
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rcs.
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tep
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raw
9 r
adii
to f
orm
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ngle
s w
ith
the
mea
sure
you
fou
nd in
Ste
p 1.
The
rad
ii w
ill in
ters
ect
the
circ
le in
9
poin
ts.
Ste
p 3
Con
nect
the
nin
e po
ints
to
form
the
no
nago
n.
1.F
ind
the
leng
th o
f on
e si
de o
f th
e no
nago
n to
the
nea
rest
ten
th o
f a
cent
imet
er.W
hat
is t
he p
erim
eter
of
the
nona
gon?
2.5
cm,P
#22
.5 c
m
2.M
easu
re t
he d
ista
nce
from
the
cen
ter
perp
endi
cula
r to
one
of
the
side
s of
the
non
agon
.3.
3 cm
3.W
hat
is t
he a
rea
of o
ne o
f th
e ni
ne t
rian
gles
for
med
?4.
125
cm2
4.W
hat
is t
he a
rea
of t
he n
onag
on?
37.1
25 c
m2
Mak
e th
e ap
pro
pri
ate
chan
ges
in S
tep
s 1–
3 ab
ove
to i
nsc
ribe
a
regu
lar
pen
tago
n i
n $
P.A
nsw
er e
ach
of
the
foll
owin
g.
5.U
se a
pro
trac
tor
to in
scri
be a
re
gula
r pe
ntag
on in
$P.
6.W
hat
is t
he m
easu
re o
f ea
ch o
f th
e fi
ve c
ongr
uent
arc
s?72
7.W
hat
is t
he p
erim
eter
of
the
pent
agon
to
the
near
est
tent
h of
a c
enti
met
er?
21 c
m
8.W
hat
is t
he a
rea
of t
he p
enta
gon
to t
he n
eare
st t
enth
of
a ce
ntim
eter
?30
.45
cm2
PN
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-3
11-3
Answers (Lesson 11-3)
© Glencoe/McGraw-Hill A11 Glencoe Geometry
An
swer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Are
as o
f Irr
egul
ar F
igur
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-4
11-4
©G
lenc
oe/M
cGra
w-H
ill62
9G
lenc
oe G
eom
etry
Lesson 11-4
Irre
gu
lar
Fig
ure
sA
n ir
regu
lar
figu
re is
one
tha
t ca
nnot
be
clas
sifi
ed a
s on
e of
the
prev
ious
ly-s
tudi
ed s
hape
s.To
fin
d th
e ar
ea o
f an
irre
gula
r fi
gure
,bre
ak it
into
fam
iliar
shap
es.F
ind
the
area
of
each
sha
pe a
nd a
dd t
he a
reas
.
Fin
d t
he
area
of
the
irre
gula
r fi
gure
.
The
fig
ure
is a
rec
tang
le m
inus
one
hal
f of
a
circ
le.T
he r
adiu
s of
the
cir
cle
is o
ne h
alf
of 3
0 or
15.
A!
lw#
$1 2$ &r2
&50
(30)
#0.
5(3.
14)(
15)2
!11
46.6
or
abou
t 11
47 f
t2
50 ft
30 ft
Fin
d t
he
area
of
the
shad
ed r
egio
n.
The
dim
ensi
ons
of t
he r
ecta
ngle
are
10
cen
tim
eter
s an
d 30
cen
tim
eter
s.T
he a
rea
of t
he s
hade
d re
gion
is(1
0)(3
0) #
3&(5
2 )!
300
#75
&
&64
.4 c
m2
5 cm
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
598.
4 ft
2
960
in2
3.4.
466
cm2
704
cm2
5.6.
1920
m2
262.
5 yd
2
7.R
efer
to
Exa
mpl
e 2
abov
e.D
raw
the
larg
est
poss
ible
squ
are
insi
de e
ach
of t
he t
hree
circ
les.
Wha
t is
the
tot
al a
rea
of t
he t
hree
squ
ares
?15
0 cm
2
15 y
d
35 y
d64
m
20 m
20 m
40 m
22 c
m
42 c
m
40 c
m38
cm14
cm
10 c
m
40 in
.
24 in
.24
in.
15 ft
34 ft
©G
lenc
oe/M
cGra
w-H
ill63
0G
lenc
oe G
eom
etry
Irre
gu
lar
Fig
ure
s o
n t
he
Co
ord
inat
e Pl
ane
To fi
nd t
he a
rea
of a
n ir
regu
lar
figu
reon
the
coo
rdin
ate
plan
e,br
eak
up t
he f
igur
e in
to k
now
n fi
gure
s.Yo
u m
ay n
eed
to u
se t
heD
ista
nce
Form
ula
to f
ind
som
e of
the
dim
ensi
ons.
Fin
d t
he
area
of
irre
gula
r p
enta
gon
AB
CD
E.
Dra
w B !
X!be
twee
n B
(#2,
3) a
nd X
(4,3
) an
d dr
aw A!
D!.T
he a
rea
ofA
BC
DE
is t
he s
um o
f the
are
as o
f !B
CX
,tra
pezo
id B
XD
A,a
nd !
AD
E.
A!
area
of !
BC
X%
area
of B
XD
A%
area
of !
AD
E
!$1 2$ (
2)(6
) %
$1 2$ (3)
(6 %
7) %
$1 2$ (2)
(7)
!6
%$3 29 $
%7
!32
.5 s
quar
e un
its
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th.
1.2.
3.
22.3
uni
ts2
12.3
uni
ts2
21 u
nits
2
4.5.
6.
19.1
uni
ts2
34.5
uni
ts2
39 u
nits
2
7.pe
ntag
on A
BC
DE
8.pe
ntag
on R
ST
UV
42.5
uni
ts2
28 u
nits
2
x
y OV
( 4, 0
)
S( –
1, 5
)
( 4, 3
)
T(2,
6)
( –2,
0)R
Ux
y O
E( 2
, –3)
B( –
2, 3
)
( 5, 0
)
C( 3
, 5)
( –3,
–2)
A
D
x
y O
G( 4
, 4)
J(1,
–2)( 4
, 0)
F(0,
6)
( –2,
4)
( –3,
0)E
KH
x
y
O
B( 4
, 4)
A( –
1, 4
)
C( 4
, –3)
( –3,
0)
Dx
y
O
W( 1
, 2)
X( 1
, –2)
Z(–2
, –2)
U( –
2, 1
)
Y(–
1 – 2, –31 – 2)
V(–
1 – 2, 31 – 2)
x
y O( 4
, 0)R
Q( 0
, 4)
S( 0
, –2)
( –3,
0)
Tx
y
ON
( 2, 0
)
M( 0
, 3)
P( 0
, –2)
L(–2
, 0)
x
y
O
F(–2
, –2)
J(2,
2)
H( 0
, 4) K( 2
, –2)
G( –
2, 2
)
x
y
O
XB
( –2,
3)
C( 4
, 5)
D( 4
, 0)
E( 0
, –2)
( –3,
0)
A
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Are
as o
f Irr
egul
ar F
igur
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-4
11-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 11-4)
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
Are
as o
f Irr
egul
ar F
igur
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-4
11-4
©G
lenc
oe/M
cGra
w-H
ill63
1G
lenc
oe G
eom
etry
Lesson 11-4
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
150
units
214
.0 u
nits
2
3.4.
38.9
uni
ts2
626.
7 un
its2
5.6.
40 u
nits
230
uni
ts2
7.8.
25.5
uni
ts2
30 u
nits
2
x
y
O
D( –
2, –
2)
G( 4
, 1)
H( 2
, –2)
E( –
2, 4
)F
( 2, 4
)
x
y
OL(
6, 0
)
M( 1
, –3)
J(1,
4)
K( 5
, 4)
x
y
O
Q( 3
, 5)
R( 6
, 7)
P( 0
, 7)
T( 3
, 2)
U( 0
, 0)
S( 6
, 0)
x
y
O
D( 8
, 5)
E( 8
, 0)
C( 3
, 8)
B( 3
, 5)
A( 0
, 0)
30
15
8
8
7
3
5
12
20
©G
lenc
oe/M
cGra
w-H
ill63
2G
lenc
oe G
eom
etry
Fin
d t
he
area
of
each
fig
ure
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
400
units
286
9.6
units
2
3.4.
143.
8 un
its2
952.
4 un
its2
5.6.
20.5
uni
ts2
22 u
nits
2
LAN
DSC
API
NG
For
Exe
rcis
es 7
an
d 8
,use
th
e fo
llow
ing
info
rmat
ion
.O
ne o
f th
e di
spla
ys a
t a
bota
nica
l gar
den
is a
koi
pon
d w
ith
a w
alkw
ay a
roun
d it
.T
he f
igur
e sh
ows
the
dim
ensi
ons
of t
he p
ond
and
the
wal
kway
.
7.F
ind
the
area
of
the
pond
to
the
near
est
tent
h.12
9.5
ft2
8.F
ind
the
area
of
the
wal
kway
to
the
near
est
tent
h.57
2.2
ft235
ft13
ft
15 ft
7 ft
x
y
OS
( 2, 0
)
Q( 2
, 6)
P( –
2, 3
)
T( –
2, 1
)
R( 4
, 3)
x
y
O
D( 2
, 5)
B( –
1, 3
)
A( –
1, 0
)
C( 1
, 4)
E( 4
, 4)
F( 4
, 0)
13
13
20
30
23
7
9
38
22
22
20
20
Pra
ctic
e (A
vera
ge)
Are
as o
f Irr
egul
ar F
igur
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-4
11-4
Answers (Lesson 11-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Rea
din
g t
o L
earn
Math
emati
csA
reas
of I
rreg
ular
Fig
ures
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-4
11-4
©G
lenc
oe/M
cGra
w-H
ill63
3G
lenc
oe G
eom
etry
Lesson 11-4
Pre-
Act
ivit
yH
ow d
o w
ind
surf
ers
use
are
a?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 11
-4 a
t th
e to
p of
pag
e 61
7 in
you
r te
xtbo
ok.
How
do
you
thin
k th
e ar
eas
of t
he f
igur
es o
utlin
ed in
the
pic
ture
of
the
sail
are
rela
ted?
Sam
ple
answ
er:T
he a
reas
get
sm
alle
r as
you
mov
efu
rthe
r up
the
sai
l.Th
e ar
ea o
f th
e tr
iang
le is
sm
alle
r th
an t
hear
ea o
f an
y of
the
tra
pezo
ids.
Rea
din
g t
he
Less
on
1.U
se d
ashe
d se
gmen
ts t
o sh
ow h
ow e
ach
figur
e ca
n be
sub
divi
ded
into
figu
res
for
whi
ch y
ouha
ve le
arne
d ar
ea fo
rmul
as.N
ame
the
smal
ler
figur
es t
hat
you
have
form
ed a
s sp
ecifi
cally
as p
ossi
ble
and
indi
cate
whe
ther
any
of
them
are
con
grue
nt t
o ea
ch o
ther
.S
ampl
e an
swer
s ar
e gi
ven.
a.b.
c.
rect
angl
e an
d sq
uare
and
re
ctan
gle
and
isos
cele
s tr
iang
letw
o co
ngru
ent
two
cong
ruen
t is
osce
les
tria
ngle
sse
mic
ircl
es
2.In
the
figu
re,B
is t
he m
idpo
int
of A
BC
!.C
ompl
ete
the
follo
win
g st
eps
to d
eriv
e a
form
ula
for
the
area
of t
he s
hade
d re
gion
in t
erm
s of
the
rad
ius
rof
the
cir
cle.
The
are
a of
cir
cle
Pis
.
m#
AB
C!
beca
use
.
mA
B!
!m
BC
!be
caus
e
.
A!B!
(B!
C!be
caus
e
.
The
refo
re,!
AB
Cis
a(n
) tr
iang
le.
AC
!,s
o A
B!
and
BC
!.
The
are
a of
!A
BC
is $1 2$
""
!.
The
refo
re,t
he a
rea
of t
he s
hade
d re
gion
is g
iven
by
A!
#!
.
Hel
pin
g Y
ou
Rem
emb
er3.
Rol
ando
is h
avin
g tr
oubl
e re
mem
beri
ng w
hen
to s
ubtr
act
an a
rea
whe
n fi
ndin
g th
e ar
eaof
an
irre
gula
r fi
gure
.How
can
you
hel
p hi
m r
emem
ber?
Sam
ple
answ
er:S
ubtr
act
whe
n th
ere
is a
n in
dent
atio
n,or
a h
ole
in t
he f
igur
e.
$$% 2$&
1 %r2
r2$1 2$ %
r2
r2r!
2"r!
2"
$ !2r2"$
or r
!2"
$ !2r2"$
or r
!2"
2r
isos
cele
s ri
ght
or 4
5°-4
5°-9
0°co
ngru
ent,
thei
r co
rres
pond
ing
chor
ds a
re c
ongr
uent
Sam
ple
answ
er:I
f tw
o m
inor
arc
s of
a c
ircl
e ar
e
Sam
ple
answ
er:B
is t
he m
idpo
int
of A
BC
!(d
efin
ition
of
mid
poin
t)
Sam
ple
answ
er:I
t is
an
insc
ribe
d an
gle
that
inte
rcep
ts a
sem
icir
cle
90%
r2
BC
AP
©G
lenc
oe/M
cGra
w-H
ill63
4G
lenc
oe G
eom
etry
Aer
ial S
urve
yors
and
Are
aM
any
land
reg
ions
hav
e ir
regu
lar
shap
es.A
eria
l sur
veyo
rs o
ften
us
e co
ordi
nate
s w
hen
find
ing
area
s of
suc
h re
gion
s.T
he c
oord
inat
em
etho
d de
scri
bed
in t
he s
teps
bel
ow c
an b
e us
ed t
o fi
nd t
he a
rea
of a
nypo
lygo
nal r
egio
n.St
udy
how
thi
s m
etho
d is
use
d to
fin
d th
e ar
ea o
f th
e re
gion
at
the
righ
t.
Ste
p 1
Lis
t th
e or
dere
d pa
irs
for
the
vert
ices
in c
ount
er-c
lock
wis
eor
der,
repe
atin
g th
e fi
rst
orde
red
pair
at
the
bott
om o
f th
e lis
t.
Ste
p 2
Fin
d D
,the
sum
of
the
dow
nwar
d di
agon
al p
rodu
cts
(fro
m
left
to
righ
t).
D!
(5"
5)%
(2"
1)%
(2"
3)%
(6"
7)!
25%
2%
6%
42 o
r 75
Ste
p 3
Fin
d U
,the
sum
of
the
upw
ard
diag
onal
pro
duct
s (f
rom
left
to
righ
t).
U!
(2"
7)%
(2"
5)%
(6"
1)%
(5"
3)!
14%
10%
6%
15 o
r 45
Ste
p 4
Use
the
for
mul
a A
!$1 2$ (
D#
U)
to f
ind
the
area
.
A!
$1 2$ (D
#U
)
!$1 2$ (
75#
45)
!$1 2$ (
30)
or 1
5
The
are
a is
15
squa
re u
nits
.Cou
nt t
he n
umbe
r of
squ
are
unit
sen
clos
ed b
y th
e po
lygo
n.D
oes
this
res
ult
seem
rea
sona
ble?
Use
th
e co
ord
inat
e m
eth
od t
o fi
nd
th
e ar
ea o
f ea
ch r
egio
n i
n s
quar
e u
nit
s.
1.2.
3.
20 u
nits
214
uni
ts2
34 u
nits
2
x
y
O
x
y
Ox
y
O
(5, 7
)
(2, 5
)
(2, 1
)
(6, 3
)
(5, 7
)
x
y
O
(2, 5
)
(2, 1
)
(6, 3
)
(5, 7
)
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-4
11-4
Answers (Lesson 11-4)
© Glencoe/McGraw-Hill A14 Glencoe Geometry
Stu
dy
Gu
ide
and I
nte
rven
tion
Geo
met
ric
Pro
babi
lity
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-5
11-5
©G
lenc
oe/M
cGra
w-H
ill63
5G
lenc
oe G
eom
etry
Lesson 11-5
Geo
met
ric
Prob
abili
tyT
he p
roba
bilit
y th
at a
poi
nt in
a fi
gure
will
lie
in a
par
ticu
lar
part
of t
he fi
gure
can
be
calc
ulat
ed b
y di
vidi
ng t
he a
rea
of t
he p
art
of t
he fi
gure
by
the
area
of
the
enti
re fi
gure
.The
quo
tien
t is
cal
led
the
geom
etri
c p
roba
bili
tyfo
r th
e pa
rt o
f the
figu
re.
If a
poin
t in
regi
on A
is c
hose
n at
ran
dom
, the
n th
e pr
obab
ility
P(B
) th
at th
e po
int i
s in
reg
ion
B,
whi
ch is
in th
e in
terio
r of
reg
ion
A, i
s
P(B
) !$a ar re ea a
o of fr re eg gi io on nB A
$.
Dar
ts a
re t
hro
wn
at
a ci
rcu
lar
dar
tboa
rd.
If a
dar
t h
its
the
boar
d,w
hat
is
the
pro
babi
lity
th
at t
he
dar
t la
nd
s in
th
e bu
ll’s
-eye
?A
rea
of b
ull’s
-eye
:A
!&
(2)2
or 4
&
Are
a of
ent
ire
dart
boar
d:A
!&
(10)
2or
100
&
The
pro
babi
lity
of la
ndin
g in
the
bul
l’s-e
ye is
!$ 14 0& 0&$
!$ 21 5$
or 0
.04.
Fin
d t
he
pro
babi
lity
th
at a
poi
nt
chos
en a
t ra
nd
om l
ies
in t
he
shad
ed r
egio
n.
Rou
nd
to
the
nea
rest
hu
nd
red
th i
f n
eces
sary
.
1.2.
0.53
0.3
3.4.
0.21
0.21
5.6.
0.5
0.58
2 cm 3 cm 1 cm
88
66
66
88
24
24
12
12
area
of
bull’
s-ey
e$
$$
area
of
dart
boar
d
2 in
.
4 in
. 4 in
.
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill63
6G
lenc
oe G
eom
etry
Sect
ors
an
d S
egm
ents
of
Cir
cles
A s
ecto
r of
a c
ircl
eis
a r
egio
n of
a c
ircl
e bo
unde
d by
a c
entr
al a
ngle
and
its
inte
rcep
ted
arc.
A s
egm
ent
of a
cir
cle
is b
ound
ed b
y a
chor
d an
d it
s ar
c.G
eom
etri
c pr
obab
ility
pro
blem
s so
met
imes
invo
lve
sect
ors
or s
egm
ents
of
circ
les.
If a
sect
or o
f a c
ircle
has
an
area
of A
squa
re u
nits
, a c
entr
al a
ngle
mea
surin
g N
°, an
d a
radi
us o
f run
its, t
hen
A!
$ 3N 60$&
r2.
A r
egu
lar
hex
agon
is
insc
ribe
d i
n a
cir
cle
wit
h d
iam
eter
12.
Fin
dth
e p
roba
bili
ty t
hat
a p
oin
t ch
osen
at
ran
dom
in
th
e ci
rcle
lie
s in
th
e sh
aded
regi
on.
The
are
a of
the
sha
ded
segm
ent
is t
hear
ea o
f se
ctor
AO
F#
the
area
of !
AO
F.
Are
a of
sec
tor
AO
F!
$ 3N 60$&
r2
!$ 36 60 0$
&(6
2 )
!6&
Are
a of
!A
OF
!$1 2$ b
h
!$1 2$ (
6)(3"
3!)!
9"3!
The
sha
ded
area
is 6
&#
9"3!
or a
bout
3.2
6.
The
pro
babi
lity
is $ar
ae ra eaof
os fe cg irm cle ent$
!$3 3. 62 &6 $
or a
bout
0.0
3.
Fin
d t
he
pro
babi
lity
th
at a
poi
nt
in t
he
circ
le c
hos
en a
t ra
nd
om l
ies
in t
he
shad
edre
gion
.Rou
nd
to
the
nea
rest
hu
nd
red
th.
1.2.
3.
0.19
0.53
0.09
4.5.
6.
0.20
0.33
0.10
44.
9460
! 56
120!
411
0!
120!
60!
4 in
.12
0!12
0!70
!50!
10 c
m
12A
D
EF
O
BC
sect
or
segm
ent
Stu
dy
Gu
ide
and I
nte
rven
tion
(con
tinu
ed)
Geo
met
ric
Pro
babi
lity
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-5
11-5
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 11-5)
© Glencoe/McGraw-Hill A15 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Geo
met
ric
Pro
babi
lity
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-5
11-5
©G
lenc
oe/M
cGra
w-H
ill63
7G
lenc
oe G
eom
etry
Lesson 11-5
Fin
d t
he
pro
babi
lity
th
at a
poi
nt
chos
en a
t ra
nd
om l
ies
in t
he
shad
ed r
egio
n.
1.0.
482.
0.37
Fin
d t
he
area
of
the
ind
icat
ed s
ecto
r.T
hen
fin
d t
he
pro
babi
lity
of
spin
nin
g th
eco
lor
ind
icat
ed i
f th
e d
iam
eter
of
each
sp
inn
er i
s 6
inch
es.
3.re
d6.
3 in
2 ,0.
2"4.
gold
12.6
in2 ,
0.4"
5.bl
ue9.
4 in
2 ,0.
3"
6.ye
llow
10.2
in2 ,
0.36
1"
Fin
d t
he
area
of
the
shad
ed r
egio
n.T
hen
fin
d t
he
pro
babi
lity
th
at a
poi
nt
chos
enat
ran
dom
is
in t
he
shad
ed r
egio
n.A
ssu
me
that
all
in
scri
bed
pol
ygon
s ar
e re
gula
r.
7.8.
16.3
uni
ts2 ,
0.14
4.9
units
2 ,0.
097
812
blue
blue
pink
red 40
!
40!30
!50
!60
!
70! 70
!re
d
yello
wyello
w
gold
blue
blue
red
gold
60!
60!
60!
100!
80!
©G
lenc
oe/M
cGra
w-H
ill63
8G
lenc
oe G
eom
etry
Fin
d t
he
pro
babi
lity
th
at a
poi
nt
chos
en a
t ra
nd
om l
ies
in t
he
shad
ed r
egio
n.
1.2.
0.50
0.45
Fin
d t
he
area
of
the
ind
icat
ed s
ecto
r.T
hen
fin
d t
he
pro
babi
lity
of
spin
nin
g th
eco
lor
ind
icat
ed i
f th
e d
iam
eter
of
the
spin
ner
is
9 m
eter
s.
3.re
d24
.7 m
2 ,0.
39
4.bl
ue23
.9 m
2 ,0.
38
5.ye
llow
15.0
m2 ,
0.24
Fin
d t
he
area
of
the
shad
ed r
egio
n.T
hen
fin
d t
he
pro
babi
lity
th
at a
poi
nt
chos
enat
ran
dom
is
in t
he
shad
ed r
egio
n.A
ssu
me
that
all
in
scri
bed
pol
ygon
s ar
e re
gula
r.
6.7.
5.5
units
2 ,0.
058
44.2
uni
ts2 ,
0.19
5
8.A
RC
HER
YA
tar
get
cons
ists
of
four
con
cent
ric
ring
s.T
he
radi
us o
f th
e ce
nter
cir
cle
is 4
inch
es,a
nd t
he c
ircl
es a
re
spac
ed 2
inch
es a
part
.Fin
d th
e pr
obab
ility
tha
t an
arr
ow
shot
at
rand
om b
y an
inex
peri
ence
d ar
cher
will
land
in a
sh
aded
reg
ion.
0.44
4 in
. 2 in
.
2 in
.
2 in
.
1711
blue
80!
40!
100!
85!
55!
blue
red
red
yello
w
Pra
ctic
e (A
vera
ge)
Geo
met
ric
Pro
babi
lity
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-5
11-5
Answers (Lesson 11-5)
© Glencoe/McGraw-Hill A16 Glencoe Geometry
Rea
din
g t
o L
earn
Math
emati
csG
eom
etri
c P
roba
bilit
y
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
11-5
11-5
©G
lenc
oe/M
cGra
w-H
ill63
9G
lenc
oe G
eom
etry
Lesson 11-5
Pre-
Act
ivit
yH
ow c
an g
eom
etri
c p
roba
bili
ty h
elp
you
win
a g
ame
of d
arts
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 11
-5 a
t th
e to
p of
pag
e 62
2 in
you
r te
xtbo
ok.
To f
ind
the
prob
abili
ty o
f w
inni
ng a
t da
rts,
wou
ld y
ou u
se g
eom
etri
cpr
obab
ility
to
com
pare
are
as o
r le
ngth
s?ar
eas
Rea
din
g t
he
Less
on
1.E
xpla
in t
he d
iffe
renc
e be
twee
n a
sect
or o
f a
circ
le a
nd a
seg
men
t of
a c
ircl
eS
ampl
ean
swer
:A s
ecto
r of
a c
ircl
e is
bou
nded
by
a ce
ntra
l ang
le a
nd it
sin
terc
ept
arc,
whi
le a
seg
men
t is
bou
nded
by
an a
rc a
nd a
cho
rd.
2.Su
ppos
e yo
u ar
e pl
ayin
g a
gam
e of
dar
ts w
ith
a ta
rget
like
the
one
sh
own
at t
he r
ight
.If
your
dar
t la
nds
insi
de e
quila
tera
l !U
VW
,you
ge
t a
poin
t.A
ssum
e th
at e
very
dar
t w
ill la
nd o
n th
e ta
rget
.The
ra
dius
of
the
circ
le is
1.C
ompl
ete
the
follo
win
g st
eps
to f
igur
e ou
t th
e pr
obab
ility
of
gett
ing
a po
int.
The
are
a of
cir
cle
Ris
.
!U
RW
is a
(n)
tria
ngle
bec
ause
R!U!
and
R!W!
are
of t
he s
ame
.
#U
RW
is a
(n)
angl
e of
the
cir
cle,
and
m#
UR
W!
.
m#
RU
X!
and
m#
RW
X!
.
The
ang
le m
easu
res
in !
RU
Xar
e ,
,and
.
R!U!
is a
of
the
cir
cle,
so R
U!
.
R !X!
is t
he le
g of
!R
UX
oppo
site
the
an
gle,
so R
X!
.
Als
o,U!
X!is
the
leg
of !
RU
Xop
posi
te t
he
angl
e,so
UX
!.
UW
!,s
o th
e ar
ea o
f !U
RW
is $1 2$
""
!.
The
n,th
e ar
ea o
f !U
VW
!3
"!
.
The
refo
re,t
he p
roba
bilit
y th
at t
he d
art
will
fal
l ins
ide
the
tria
ngle
is t
he r
atio
of
to
,whi
ch is
app
roxi
mat
ely
(to
the
near
est
thou
sand
th).
Hel
pin
g Y
ou
Rem
emb
er3.
Man
y st
uden
ts f
ind
it d
iffi
cult
to
rem
embe
r a
larg
e nu
mbe
r of
geo
met
ric
form
ulas
.How
can
you
use
the
form
ula
for
the
area
of
a ci
rcle
to
find
the
are
a of
a s
ecto
r of
a c
ircl
ew
itho
ut h
avin
g to
lear
n a
new
for
mul
a?S
ampl
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PE
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11-5
11-5
Answers (Lesson 11-5)