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11-1
Practice
5.5 ft
h parallelogram.
12 mm
Find the perimeter
and area and
of each
or triangle.
to Round
the
Find
the perimeter
areaparallelogram
of each parallelogram
or Round
triangle.
to the
4 ft
2. nearest
3. 1)
3.5
m 2),
if necessary.
40. tenth
W(1,
X(1, 6),
Y(4,
nearest
tenth
if necessary.
2.
41. A(-8, 0), B(-7, 4), C(-3, 3)
4m
3. 60Лљ
Areas
and Triangles
3.5 of
m Parallelograms
___________________________________ Hour _______
2.4),parallelogram
3. Coordinate
Geometry
the -2)
area of the
Example
2 K(-7,
D(0,
E(2,
4), of
F(6,
G(6,2.0) Name
-2), L(-7,
6), M(1, Find
6), N(7,
4.7or
in.43.
Find 1.
the42.
perimeter
area
each
triangle.
Round
to the
1. 0),and
3.
8
cm
5.7
in.
10 in.
5m
8
cm
4.7
in.
10 in.
5m
nearest tenth if necessary.
11-1 Areas5.7
of in.
Triangles
and
Parallelograms
(page
349)
10 mm
60Лљ
1.
4. A(2, 0), B(7, 0), C(8, 4), D(3, 4)
Worksheet
45Лљ
45Лљ
60Лљ
11
m m of each
10 cm
Find the5.8
area
5.8 m 11 m2. figure.6 in.
Lesson 11-1
18 mm
45Лљ
3.
10 cm
45Лљ
6.
I(2, 2), J(4, 2), K(2, -3), L(0, -3)
8 cm
Find
triangle 6isin.
shaded, just find the area10of
in. the shaded part. A=1/2bh
5 m the area of each Triangle. If the
44.
14 yd1.
4.
d
11 m
4m 4m
25 ft
60Лљ
4.45Лљ
2.
5.
4.
45.
10
22 cm
in.
26 in.
15 cm
Example 3
21 cm
5.
(page 350)
25 ftparallelogram with the45Лљgiven vertices.
ind the area of the
try Find
45Лљ
cm
the17area
NAME
4. D(3,
4),
D(3,
4) 4)
C(8,
4),
NAME
11-1
25 15
ft25cmcm
20 cm
20 in.
Skills Practice
25 cm
3.
7.
200 m
Find the value of h for each parallelogram.
6.
8.
9.
120 mh
12.8 ft
PERIOD
DATE
5. 0), 0),
5. E(-4,
0), F(-1,
G(1,
-3),
H(-2,
-3)
5. E(-4,
0), F(-1,
G(1,
-3),
H(-2,
-3) 6.
20 in.
6. 0),0),
m
18.5
km
3),
L(0,
-3) -3) 7. M(-6,
-1),
N(-5,
P(1,
0),0),
Q(0,
-1)
(2,3.4-3),
L(0,
7. M(-6,
-1),
N(-5,
P(1,
Q(0,
-1)
17 cm
6.
of the
parallelogram with the given vertices.
17 cm
15 cm
46.
45Лљ
5.
DATE
14
12.8 ft
0.3
40 m
8 ft
PERIOD
8 ft
60 m
8
10
The
Greek mathematician
Heron is most famous for this formula
11-1 History
Skills
Practice
Areas
ofancient
Parallelograms
and Triangles
for the area of a triangle in terms of the lengths of its sides a, b, and c.
enge
15 cm
or each
parallelogram.
ach
parallelogram.
25 cm
9 km
12 in. 20 in.
12 16
in. in.
12.8 ft
16 in.
8 ft
4 ft
46ftft
6 ft
Find4. the
of10.
each
5. parallelogram or triangle.6.Round to the
9. perimeter and area10.
9.
the area
of each shaded triangle.
Example
0.52 a)(s 2 12b)(s
nearest tenth
0.5
4+
ft b + c)
6 ft
in.
A if=necessary.
"
s(s
s 4= 12(aFind
13in. h2hc)16, where
30 cm
0.3
13
7.
of aheight
parallelogram
its 350)
base.
thebase.
area of the
0.3The height
8. is 5 feet more
(page
7. The
of a parallelogram
is 5 than
feet
more
thanIf its
1212
60Лљ
h 204 square
11. If the area of the
12.
1.
2.
h
parallelogram
is
feet,
find
its
base
and
height.
20 cm
parallelogram
is 204area
square of
feet,each
find its base
and height.
4.5
yd
Find
the
perimeter
and
parallelogram
or
triangle.
Round
5.5 ftthe area 5.7
18 17 in. to find
m
5 m Round your
Use Heron’s
Formula
and
a
calculator
of
each
triangle.
10
18
0.4 0.4
12 mm
Areas of Parallelograms and Triangles
h shaded
7. triangle.
49. a = 6 cm, b = 7 cm, 8.
c = 11 cm
5.5ft,ft c = 11 ft
9. b = 10.2
50. a = 10 ft,
Lesson 11-1
1.
Skills
Practice
Copyright В© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
parallelogram is 204 square feet, find its base and height.
60Лљ
8. The18height
of aheight
parallelogram
is three
its17
base.
Ifits
the
thearea
The
of9a in.,
parallelogram
is three
the
of the
parallelogram
13
in.times
in.times
mm8.
10 mm
m 17
47.
a
=
8
in.,
b
=
c
=
10
in.
48.
a base.
=area
15Ifofm,
b4parallelogram
=
m,3 m
c = 21 m
2.
is 972 square
inches,
find
its
base
and
height.
is 972 square inches, find its base and height.
Copyright В© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4m
Copyright В© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
nearest
tenth
ifthenecessary.
7. The height
of ato
parallelogram
5 feetDATE
more
than 4its
the area of the
ft base. IfPERIOD
answer
nearestis whole
number.
7.
Example
ded 8.
triangle.
12 mm
Theof
height
of a parallelogram is three
times
its base.
If the5area of14.
theLandscaping
parallelogramTaisha’s Bakery has a pla
Areas
Parallelograms
and
Triangles
height of12.
a parallelogram is 10 feet more
13.than its base. If the area of the
ft parking lot. The four par
(page 351)
is 97251.
square
inches,
find its Formula
base and height.
4aft50 ft-by-31
a.square
Use
Heron’s
to
find
the
area
of
4.5
yd
9.
The
base
of
a
triangle
is
four
times
its
height.
If
the
area
of
the
triangle
is
allelogram
is
1200
feet,
find
its
base
and
height.
12.
13.
rimeter
and
area
of
each
parallelogram
or
triangle.
Round
to
the
6
yd
9.
The
base
of
a
triangle
is
four
times
its
height.
If
the
area
of
the
triangle
is
m
spaces
are congruent
parallelograms, the
4.5242
yd square
15
in.
millimeters,
find
its
base
and
height.
26
in.
the
triangle
at
the
right.
3.
4.
3
ft
6
yd
242
square
millimeters,
find
its
base
and
height.
th if necessary.
9
in.
14 yd
60Лљ is a rectangle, and the two unpav
region
mm
10
mm to part (a) by
3 in.ftusing the
b.18Verify
your
answer
22
for
7.5 yd
9. The base of is
a triangle
times
height.
the
area
of the
is flowers are congruent triangles.
one half is
of four
its height.
If the
area Ifof
the
triangle
is triangle
196 see
square
1 2. its
m base of 7aydtriangle7.5
12 Practice.
in. area of the surface to be pav
For
more
practice,
Extra
formula
A
=
bh.
45Лљ
45Лљ
yd
a. Find
the
242
square
millimeters,
find its
2 ftheight.
2 base and
5.52 ftft
limeters,
find
its base
and height.
10. FRAMING
A rectangular
poster measures
42 inches by 26 inches. A frame
shop
fittedshop fitted
1210.
mmFRAMING
A rectangular
inches.
A
frame
blem Solving
the
areas of the driving region
2 ft poster
2 ftmeasures 42 inches by 26 adding
the
poster
with
a
half-inch
mat
border.
4 ft
isha’s Bakery has a plan
for with a half-inch
the poster
mat
border.
For
moreFor
practice,
see
Extra
Practice.
spaces.
more practice,the
seefour
Extraparking
Practice.
Find
the area
ofparking
each Parallelogram. A=bh
lot.has
The
sarking
Bakery
a four
plan
for
a. Find
the
area
of
the
poster.
60Лљ
b.
Describe
another
method for finding
a. Find theposter
area ofmeasures
the poster.
10. Problem
FRAMING
A
rectangular
42 inches by 26 inches. A frame shop fitted
m
Solving
mm
10 mm
eple
and
Solving
Find
the
area
of driving
each parallelogram.
uent
parallelograms,
the
5.
6.
3.4
m
18.5 km
ng lot. The
four
parking
10. poster
11.
12. area of the surface to be paved.
the
with
a half-inch
mat
border.
b. Find
the
ofthe
thearea
mat of
border.
b.area
Find
the mat border.
ngle,
and
the
two
unpaved
areas
10 ft3.5 m 9 km
1.
2.
3.
the driving
eparallelograms,
13.
c. Use your method
26 in.from part (b) to fin
4. marked
a. Find
the
area
of
the
poster.
ice
by Example
ongruent
triangles.
Find
the
area
of
each
parallelogram.
c.
Suppose
the
wall
is
marked
where
the
poster
will
hang.
The
area
includes
14
yd
15
cm
c.12
Suppose
the wall is marked where the poster will hang. the
marked
area
includesanswers from
the area
of each
parallelogram.
49)Find
and
the two
unpaved
areas
cm
area.
Then
compare
10 ft the poster and frame. Find the The
an
additional
12-inch space
around
total
wall
area
of the surface
to
bearea
paved
by
an
additional
12-inch
space
around
the
poster
and
frame.
Find
the
total
wall
area
4.7
in.
b.
Find
the
of
the
mat
border.
22
in.
1. been marked for
2.
3. 5.7parts
Example
1that has
uent1.
triangles.
3.5 m
50 the
ft poster.
your work.
in. (a) and (b) to check
2.
3.
3.5
m
that
has
been
marked
for
the
poster.
eas of(page
the driving
region
and
20
cm
15
cm
349)
12 cmwhere the poster will
7 yd
e surface
to
be paved
by is marked
c.
Suppose
the wall
hang. The marked area includes
26 m
in.
15
cm
5.8
4.
ng
50
4.7 in.
45Лљftaround
30 cm12 cm
yd spaces.an additional
5.7 in.
6Geometry
in.45Лљ
12-inch
space
the
poster
and
frame. Find
the total
wall
area
fther
the7.
driving
region
and
11
7
Glencoe
8.
Standardized
Test
Prep
4.7
in.
60Лљ
method
for
finding
the
20
cm
22
in.
5.7 in.
that has been marked
for the poster.
paces.
5.8 m
20 cm 20 cm
rface to be paved.
6 in.
in.
45Лљ
445Лљ
m of 5.8
m triangle17are
method
for
finding
Choice
52. The lengths of the sides
a right
10 in., 24 in., and 26 in.
hodMultiple
from
part
(b) tothe
find
6 in.
What is the area of 15
thefttriangle?
be paved.
Chapter
11 Chapter
8
Glencoe Geometry
nto
compare
answers
from
11
8
Glencoe Geometry
4parallelogram
m
2 the area
2
2 15.
10:57:11 AM
13.
14. B.
Coordinate Geometry
Find
of120
the
with
the
given6/1/09
vertices.
erom
2 part
in.
C.
130
in.
D.
156 in.2
A.
116
in.
31
ft
(b)your
to find
(b) to check
work.
PDF
Pass
13 in.
17 in.
49)5.
15
6.
4Find
mft
3.4
m
18.5
km C
53.0),
What
is4),
theD(3,
area4)
of
$ABCD
atofthe
D
mpare
answers
4. A(2,
0),Coordinate
B(7,
C(8,
5. E(-4,
0),
F(-1, 0),
G(1,
-3),
-3)
Geometry
the area
theright?
parallelogram
with
theH(-2,
given
vertices.
Example
2 from
Lesson
7-1
Areas
of
Parallelograms
and Triangles
351
Chapter 11
8
Glencoe
Geometry
2
2
6.
18.5
G.31
64ft
in. km
F. 32 in.
(page
349)work.
o check
your
Lesson
7-1
Areas
o
4.
A(2,
0),
B(7,
0),
C(8,
4),
D(3,
4)
5.
E(-4,
0),
F(-1,
0),
G(1,
-3),
H(-2,
-3)
6. I(2,Geometry
2), J(4,
2), H.
K(2,
-3),
7.
M(-6,
-1), N(-5,
0), P(1,
0), Q(0,8 -1)
2L(0,
Coordinate
Find
the
area-3)
of I.the45.6
parallelogram
with the
given
001_025_CRMGEOC11_890520.indd
8
6/1/09 10:57:18 AM
91.2
in.
in.2
in.
9 km vertices.
001_025_CRMGEOC11_890520.indd 8
6/1/09
11.3 in.
Lesson 11-1
CISES
Pass
9 feet
km more than its base. If the area of
9. The height of 6.
a parallelogram
is 10
the0), Q(0,
PDF
I(2, 2), J(4, 2), K(2,
-3),
L(0, -3)
7. M(-6, -1), N(-5, 0), PDF
P(1,
-1)
A for
parallelogram
176 ft0), G(1, -3), H(-2, -3)
A(2,
B(7,
0),
C(8,
4),
D(3,parallelogram.
4) has
5.
0),of
F(-1,
is54.
1200
square
feet,
findadjacent
itsE(-4,
basesides
and
height.
Find0),the
value
of
h
each
e 3 4. parallelogram
A 8 in. B
and 312 ft. The altitude to the shorter side is
5_CRMGEOC11_890520.indd 8
50)
Find
the
value
of
h
for
each
parallelogram.
Example
3
6. I(2,8.2), J(4, 2), K(2,290
-3), L(0, -3)
7.ofM(-6,
-1), N(-5,
is the area
the parallelogram?
10. 0), P(1, 0), Q(0, -1)
h ft. What2 9.
0.5
2
(page 350)
B.
51,352
ft
C.
54,912
ft2 h
D. 55,202 ft2
A.
51,040
ft
13 10.
8.14
0.3 9.
12 square
h
m 10. The base of a triangle
0.5 of the triangle is 196
is one half
8. of its height.hIf the area
13
PDF Pass
Pass
6/1/09 10:57:18 AM
11-1
Practice
Areas ofAreas
Parallelograms
and Triangles
ofParallelograms
Parallelograms
andTriangles
Triangles
3.
Areas
of
and
of Parallelograms
and Round
Triangles
e perimeter andAreas
area of each
parallelogram or triangle.
to the
14 yd
Find
the
perimeter
andarea
areaofofYou’ll
each
parallelogram
triangle.
Round
the
Find
the
area of eachand
Parallelogram.
need
to use Special Right
Triangles
orRound
Trig.
A =to
bhto
Find
the
perimeter
each
parallelogram
oror
triangle.
the
tenth
if
necessary.
Find the
perimeter
and area of each parallelogram or triangle.
Round to the
7 yd
nearest
tenth
necessary.
nearest
tenth
ififnecessary.
DATE
PERIOD
45Лљ
16.
17.
18.
nearest tenth if necessary. 2.
1.
1.
1.55mm
5.5 ft
2.2.
2.8 4cm
8ftcm
12 mm
5m
60Лљ
60Лљ
ams
60Лљ
18 mmand 10Triangles
mm 11
11mm
11 m
3. 3.
3.
8 cm
45Лљ
45Лљ
60Лљ
45Лљ
1010
cmcm
10 cm
5.
arallelogram or triangle. Round to the
15
15cm
cm
15 cm
22 in.
7.
60Лљ
20 cm
35. Probability Ann drew
these three figures on a grid. A fly 12.8
lands
ft ftat random at a
12.8
45Лљ
8 ft 8 ft
12.8 ft
point on the grid.
8 ft
2020
in.in.
2525cm
cm
25 cm
20 in.
Lesson 11-1
17
174cm
cm
ft
17 cm
60Лљ 45Лљ
Copyright В© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
35.
2. Probability Ann drew these three figures on a grid. A fly lands at random at a
4.
5.5.
6. 6.
4. point on 5.5
26 in.
theft grid.
4.5.
6.
30 cm
14 4.
yd
.4 m
Лљ
35. Probability Ann drew these three figures on a grid. A fly lands at random at a
20.
21.
point on the grid.
Lesson 11-1
19.
10 in.
10 in.
10 in.
3.4
45Лљ
45Лљm
45Лљ
21. The height of a parallelogram is 5 feet more than its base. If the area of the parallelogram is 204 square feet, find its
6.
base and height.
4 ft
6 ft
12 in. 18.5 km
16 in.
12 in.
16 in.
4 ft
6 ft
4 ft
6 ft
12 in.
16 in.
a. Writing
Is the fly more
9 km likely to land on one of the figures or on the blank
26 in.
4.
a. Writinggrid?
Is theExplain.
fly more likely to land on one of the figures
or on
the blank
9. The
height
of a parallelogram is 10 feet m
22 in.
parallelogram
1200 likely
squareto
feet, find it
grid?b.Explain.
Suppose you know the fly lands on one of the figures.
Is the flyismore
7.
height
of
a
parallelogram
is
5
feet
more
than
its
base.
If
the
area
of
the
45Лљ
7.7.The
The
height
of
a
parallelogram
is
5
feet
more
than
its
base.
If
the
area
of
the
22.
The
height
of a
parallelogram
is Is
3lands
times
its
base.
Ifof
the
area
ofits
thebase.
parallelogram
is
972 likely
square
find its base
b. Suppose
you
know
the
fly
on
one
the
figures.
Isone
the
fly
tothe blank
land
one
figure
than
on
another?
The
height
of
aon
parallelogram
is 5fly
feet
more
than
Ifofthe
area
ofor
the
a.
Writing
the
more
likely
toExplain.
land
on
themore
figures
oninches,
30 cm parallelogram is 204 square feet, find its base and height.
and height.
parallelogram
204
square
find
base
8.
land on oneisis
figure
than
onfeet,
another?
Explain.
parallelogram
204grid?
square
feet,
findits
its
base and
and height.
height.
Explain.
20 cm
find its base and height.
land on
figure
on another?
Explain.
Coordinate
Geometry Find
theone
area
of athan
polygon
with the
givenmillimeters,
vertices.
6.
18.5 km
36.
A(3,
9),
B(8, 9), C(2, -3),
D(-3,
-3)
37.
E(1,
1),
F(4,
5),of
G(11,
5), H(8, 1)
8.
height
of
aaparallelogram
isisthree
times
itsitsbase.
If If
the
area
of
the
parallelogram
8.8.The
The
height
of
parallelogram
three
times
base.
the
area
the
parallelogram
36.
A(3,
9),
B(8,
9),
C(2,
-3),
D(-3,
-3)
37.
E(1,
1),
F(4,
5),
G(11,
5),
H(8,
1)
The
height
of
a
parallelogram
is
three
times
its
base.
If
the
area
of
the
parallelogram
23.
base ofinches,
a triangle
is fourits
times
its height.
If the
the area
ofofthe
is with
242 square
millimeters,
find its base and
Coordinate
Geometry
Find
area
a triangle
polygon
the given
vertices.
9 kmThe
is
square
find
base
and
height.
13 in.
17 in.
isis972
972
find
its
height.
38.square
M(-2,inches,
-5), L(1,
N(2,and
-2)height.
972
square
inches,
find-5),
itsbase
base
and
height. 39. R(-7, 2), S(-3, -1), T(3, -1)
38. M(-2, -5), L(1,
-2)
39.D(-3,
R(-7,
2), S(-3,
-1),
T(3,5),
-1)
36.-5),
A(3, N(2,
9), B(8,
9), C(2, -3),
-3)
37. E(1,
1), F(4,
G(11, 5), H(8, 1)
40. W(1, 2), X(1, 6), Y(4, 1)
41. A(-8, 0), B(-7, 4), C(-3, 3)
38.Y(4,
M(-2,
-2) 0), B(-7,
39. R(-7,
2), S(-3,
40. W(1, 2), X(1, 6),
1) -5), L(1, -5), N(2,
41. A(-8,
4), C(-3,
3) -1), T(3, -1)
eight of a parallelogram is 10 feet more than its base. If the area of the
9.
base
of
aa0),
triangle
isis2),
four
times
its 1)
height.
IfIfthe
area
ofof
the
triangle
isC(-3,
D(0,
E(2,
4),
F(6,
4),
G(6,
0)
43.
K(-7,
-2),
L(-7,
6),
M(1,
6),
9.9.
The
base
of
triangle
four
times
height.
the
area
the
triangle
is
40.
W(1,
X(1,
6),
Y(4,
41.
A(-8,
0),
B(-7,
4),
3) N(7, -2)
8.The
lelogram
is42.
1200
square
feet,
find
its
base
andits
height.
42.
D(0,
0),
E(2,
4),
F(6,
4),
G(6,
0)
43.
K(-7,
-2),
L(-7,
6),
M(1,
6),
N(7,
The
base
of
a
triangle
is
four
times
its
height.
If
the
area
of
the
triangle
is-2)
242
square
millimeters,
find
its
base
and
height.
Find
each
area.
You
will
have
to
divide
the
figure
into
triangles
and
parallelograms,
then
add
the
areas together.
242
find its
base
and
height.
242square
squaremillimeters,
millimeters,
base4),
and
42. D(0, 0),find
E(2, its
4), F(6,
G(6,height.
0)
43. K(-7, -2), L(-7, 6), M(1, 6), N(7, -2)
17 in.
Find
each figure.
24.the
25.
26.
Find
areathe
of area
each of
figure.
ase of a triangle is one Find
half the
of its
height.
If the
area of the triangle is 196 square
area
of each
figure.
Chapter46.
11
44.
45.
m
25
ft
15 cm by46.
44.FRAMING
45.
meters,
find its base
height. poster
m shop200
25 ft
15 cm 42 inches
10.
A and
rectangular
measures
26 inches. A 200
frame
fitted
10.
FRAMING
AArectangular
poster
measures
by
A
fitted
13 in.
17 in.
44.
45. 42
46.
200 m
21 cm
ft 21 cm
15 cm
10.the
FRAMING
rectangular
poster
measures
42 inches
inches
by 26
26 inches.
inches.
A frame
frame shop
shop
fitted
poster with
a half-inch25mat
border.
the
poster
with
a
half-inch
mat
border.
21 cm
the poster with a half-inch mat border.
120 m
120 m
25 ft 25 ft
a. Find the area of 25
theft poster.
120 m
a.a. Find
Findthe
thearea
areaofofthe
theposter.
poster.
001_025_CRMGEOC11_890520.indd 7
40 m
40 m
t more than its base. If the area of the
40 m
b. Find the
area
of
the
mat
border.
60 m
25
ft
20
cm
60
m
25
ft
20
cm
b.b.and
Find
the
area
of
the
mat
border.
its base
height.
60 m
25 ft border.
20 cm
Find the area of the mat
c. Suppose the wall is marked where the poster will hang. The marked area includes
c.c.
Suppose
the
wall
isisThe
marked
where
the
poster
will
hang.
The
area
includes
History
The ancient
Greek
mathematician
Heron
isand
most
famous
formarked
this
formula
the
wall
marked
where
the
poster
willframe.
hang.
The
marked
area
Challenge
ngeC
History
ancient
Greek
mathematician
Heron
is
most
famous
for
this
formula
History
The
ancient
Greek
mathematician
Heron
is most
famous
for
this
formula
anSuppose
additional
12-inch
space
around
the
poster
Find
the
total
wall
area
an
additional
12-inch
space
around
the
poster
and
frame.
Find
the
total
wall
area
an
additional
12-inch
space
around
the
poster
and
frame.
Find
the
total
wall
for
the
area
of
a
triangle
in
terms
of
the
lengths
of
its
sides
a,
b,
and
c.
for
areafor
ofisthe
a196
triangle
inof
terms
the lengths
ofsides
its sides
andc.c.
marked
poster.
height. Ifthat
the
area
of the
triangle
square
forhas
the been
area
ofthe
a triangle
in
terms
theoflengths
of its
a, a,
b,b,and
that
thathas
hasbeen
beenmarked
markedfor
forthe
theposter.
poster.
72c)a)(s
Glencoe
A2=b)(s
"s(s2
21c)
, where+
=
(a + bGeometry
A = "A
s(s=2"a)(s
,
where
c) 12+
2(a +s b
s(s 2 a)(s 2 b)(s 2
2 b)(s
c)s ,=
where
= 12s (a
b ++
c) c)
Use and
Heron’s
Formula and
a calculator
find
thetriangle.
area of each
triangle.
Use Heron’s Formula
a calculator
to find
the areatoof
each
Round
yourRound your
Use Heron’s
Formula
and
a
calculator
to
find
the
area
of
each
triangle.
Round your
answer
to the
nearest whole number.
answer to the nearest
whole
number.
answer to the nearest whole number.
47. a = 8 in., b = 9 in., c = 10 in.
48. a = 15 m, b = 6/1/09
17 m,10:57:11
c =AM21 m
Chapter
PDF
Pass
47. a 11
= 8 in., b = 9 in., c = 10 in.
48.8a = 15
m, b =
17 m, c = 21 m Glencoe Geometry
Chapter 11
8
Glencoe Geometry
Copyright©©Glencoe/McGraw-Hill,
Glencoe/McGraw-Hill,aadivision
divisionofofThe
TheMcGraw-Hill
McGraw-HillCompanies,
Companies,Inc.
Inc.
Copyright
Copyright В© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
base
triangle
is onetohalf of its he
b. Suppose Find
you know
the flyoflands
on one of10.
theThe
figures.
Is of
thea fly
more likely
Coordinate Geometry
the area
17 in. a polygon with the given vertices.
12
8 cm
8 cm
87В°
87В°
Findprocess
the area
trianglewith
using
6 SAS
cm method.
This
canofbeeach
generalized
the the
following
formula:
6 in
140В°
6 in
140В°
6 cm
T H E AREA FORM UL A FOR A T RI ANGL E
A
For a triangle with side lengths a, b, and c, and
opposite angles of A, B, and C, the area is given by:
b
c
Name___________________________________
1
Area
2
ab sin C
Date________________ Period____
C
B
a
Exercise
#2: Which of the following represents
the exact area, in square inches,29.of an equilateral triangle
27.
28.
r to the
nearest
tenth.
whose
sides have
a length of 10 inches?
3)
2)
(1) 50 2
8 yd
3)98В°
(3) 25 2
5 in
4)
Dr. Neal, WKU
3 yd
4)
8 yd
Scalene Triangles
and Heron’s Formula
98В°
140В°
3 yd
n 3.2 Area 6 in
Name___________________________________
3
3 Heron’s Formula gives the area
a , b , and (4)
c . 25
e has sides(2)of10length
Then
ng Heron's Formula
Date________________ Period____
le to
4 in
96В°
7 in
96
AL GEBRA 2 W I T H T RI GONOM ET RY , UNI T #9 В± T RI GONOM ET RI C APPL I CAT I ONS В± L ESSON #1
the area
of each triangle using
eM AT HHeron’s
I NST RUCT I Formula.
ON, RED H OOK , NY 12571, В© 2009
theFind
nearest
tenth.
Area
s(s ! a)(s ! b)(s ! c)
3) - WS Section
3.2= Area
2)
E
Name___________________________________
2
of each
to -the
nearest
tenth.
14 ft
Mr.triangle
Butera
Area
using
Heron's
16 ft
30.
31.
Date________________
Period____
Name___________________________________
Formula
Date________________ Period____
2) sides that measure 6 yd and
5) A
triangletowith
Find the area of each
triangle
the two
nearest
6 fttenth.
D
E
2 yd with an included angle of 10В°.
F
1)4 inof the following triangle:
2)
he area
6) A triangle with two sides that measure 6 m a
8 m with an included angle of 137В°.
Z
6 ft that
5) A triangle with twoE sides
D measure 6 yd and
14
ft
2 yd16with
an included angle of 10В°.
ft
Z
4)
6 in
X
n
4 in
14
Y
12
4 in
X
7 in
7 in
D
6 ft
1 Formula
a - Area
using
Heron's
PreCalc
(M453)
- WS
Area
where
s = Section
(a + b3.2
+ c)
6) A triangle with two s
8 m with an included
14 ft
16 ft
F
96В°
7 in
20triangle with two sides that measure 5 cm and
7) A
8 cm with an included angle of 39В°.
32.
F
8) A triangle with two sides that measure 8 ft an
7 ft with an included angle of 30В°.
(12 + 14 + 20) = 23. Then4)the area is 7) A triangle with two sides that measure 5 cm and
A
8 cm with an included angle of 39В°.
16 mi
0)(23 ! 14)(23 ! 12) =
16 km
m
5 in
5 in
23 ! 3 ! 9 ! 11 =
C
12 mi
6831
9 mi ! 82.65 sq. units.
4)
B
A
6) A triangle
with
two
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3) 8 m with an included angle of 137В°. 16 mi
4)
F
D
14 km
C
12 mi
11 km
Wo
A
16 mi
B
В©5 i2t0q1522 vKMuMtxah 4SSoifKtNwxa5rSe6 TLOLiCr.a 9 5AtlVlU rr0i3gghHtNsH Trme2svefrrvSe1dD.z P JM0azdeeg ewJirtzhF kI6ntfXionkiht8eM aG0ero9Lmmi
3eptaroyL.o
C
E
-1-
9 mi
16 km
D
8) A triangle with two s
7 ft with an included
12 mi
B
-1-
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