Use with Lesson
5-Minute Check
1. Find the value of x in
the figure.
57˚
11-1
(over Chapter 10)
2. Classify the triangle
by its angles and by
its sides.
90˚
x˚
3. Find the value
of x in the pair
of similar figures.
4 cm
14 cm
0.5 cm
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4.
x
Triangle NLR has vertices N(2, 2),
L(1, 4), and R(1, 2). If Triangle NLR has vertices
N(-2, 2), L(-1, 4), and R(-1, 2), what type of
reflection was performed on triangle NLR?
Test Practice
A ΔNLR was reflected over the x-axis.
B ΔNLR was reflected over the y-axis.
C ΔNLR was reflected over both axes.
D ΔNLR was not reflected.
ANSWERS
1. 33
3. x = 1.75
Chapter 11
2. acute; isosceles
4. B
Glencoe Math Connects, Course 2
Area of Parallelograms
11–1
GLE: ME:1B,2E
BUILD YOUR VOCABULARY (pages 255–256)
MAIN IDEA
• Find the areas of
The base is any
of a parallelogram.
parallelograms.
The height is the length of the segment
KEY CONCEPT
Area of a Parallelogram
The area A of a
parallelogram equals the
product of its base b and
height h.
to the
EXAMPLE
with endpoints on
sides.
Find the Area of a Parallelogram
Find the area of the parallelogram.
6.4 cm
7.5 cm
A=
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Estimate
A = bh
A=
A=
·
or
cm 2
Area of a parallelogram
·
Replace
with 7.5 and
with 6.4.
Multiply.
The area of the parallelogram is
square centimeters.
This is the same as the estimate.
Check Your Progress Find the area of the parallelogram.
HOMEWORK
ASSIGNMENT
Page(s):
4 in.
13 in.
Exercises:
Math Connects, Course 2
257
Score:________/________
10-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
11-2
(over Lesson 11-1)
Find the area of each parallelogram. Round to
the nearest tenth if necessary.
1.
2.
7 yd
19 in.
12 yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11 in.
3. Determine whether the following statement is
true or false. The height of a parallelogram is the
distance from the base to the opposite side.
4.
What is the height of a
parallelogram if the base is 24 centimeters
and the area is 744 square centimeters?
Test Practice
A 28 cm
C 31 cm
B 30.5 cm
D 32 cm
ANSWERS
1. 209 in2
3. true
Chapter 11
2. 84 yd2
4. C
Glencoe Math Connects, Course 2
11–2
Areas of Triangles and Trapezoids
GLE: ME:1B,2E
EXAMPLE
MAIN IDEA
Find the Area of a Triangle
Find the area of the triangle below.
• Find the areas
of triangles and
trapezoids.
3.2 cm
9 cm
KEY CONCEPT
Area of a Triangle The
area A of a triangle
equals half the product
of its base b and height h.
1
Estimate _
(9)(3) =
2
1
A=_
bh
Area of a triangle.
1
A=_
Replace b with
A=
Multiply.
2
2
and h with
.
.
The area of the triangle is 14.4
This is close to the estimate.
4.5 ft
6 ft
EXAMPLE
Find the Area of a Trapezoid
Find the area of the trapezoid below.
4m
3m
7.6 m
258
The bases are
meters and
The height is
meters.
Math Connects, Course 2
meters.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Your Progress Find the area of the triangle below.
11–2
KEY CONCEPT
Area of a Trapezoid The
area A of a trapezoid
equals half the product
of the height h and the
sum of the bases b 1
and b 2.
1
A=_
h(b 1 + b 2)
Area of a trapezoid
1
(3)
A=_
Replace h with
, b 1 with
and b 2 with
.
2
2
1
A=_
2
A=
(11.6)
Add
and
,
.
Multiply.
The area of the trapezoid is
square meters.
Check Your Progress Find the area of the trapezoid below.
8 cm
6 cm
®
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ORGANIZE IT
Under the tab for
Lesson 11-2 of your
Foldable, record in words
and symbols how to find
the area of triangles and
trapezoids.
12.5 cm
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
Math Connects, Course 2
259
Score:________/________
10-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
11-3
(over Lesson 11-2)
Find the area of each figure. Round to the
nearest tenth if necessary.
1.
2.
8 cm
4 cm
7 in.
6 cm
12 in.
3.
13.2 m
4. triangle:
base = 15.75 yd
height = 10.25 yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
24 m
5. Bell has a triangular garden with a base of
20 feet and a height of 15 feet. Find the area
of Bell’s garden.
6.
A trapezoid has bases of
14.7 meters and 12.2 meters, and a height of
9 meters. What is the area of the trapezoid to
the nearest tenth?
Test Practice
A 132.3 m2
C 144.6 m2
B 121.1 m2
D 155.8 m2
ANSWERS
1. 42 in2
4. 80.7 yd2
Chapter 11
2. 28 cm2
5. 150 ft2
3. 158.4 m2
6. B
Glencoe Math Connects, Course 2
11–3
Circles and Circumference
GLE: ME:2C
BUILD YOUR VOCABULARY (pages 255–256)
MAIN IDEA
A circle is a set of all points in a plane that are the
• Find the circumference
distance from a given
of circles.
called the
center.
The diameter (d) is the distance
a
through its center.
The circumference (C ) is the distance
a circle.
The radius (r) is the distance from the
to any
.
point on a
An approximation often used for π (pi) is
Circumference of a Circle
The circumference C of
a circle is equal to its
diameter d times π, or 2
times its radius r times π.
Find Circumference
PETS Find the circumference around the hamster’s
running wheel shown. Round to the nearest tenth.
C = 2πr
r 3 in.
C=2
C=
(3)
Multiply.
The circumference is about
260
Math Connects, Course 2
inches.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
KEY CONCEPT
EXAMPLE
.
11–3
REMEMBER IT
All circumferences
are estimates since 3.14 is
an estimated value of pi.
Check Your Progress SWIMMING POOL
A new children’s swimming pool is being built
at the local recreation center. The pool is
circular in shape with a diameter of 18 feet.
Find the circumference of the pool. Round to
the nearest tenth.
EXAMPLE
18 ft
Find Circumference
Find the circumference of a circle with a diameter of
49 centimeters.
Since 49 is a multiple of 7, use
for π.
C = πd
Circumference of a circle
22
·
C≈_
Replace
7
22
with _
and d with
7
.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7
22 _
C≈_
· 49
7
1
C≈
1
Divide by the
, 7.
Multiply.
The circumference is about 154
.
Check Your Progress Find the circumference of a circle
with a radius of 35 feet.
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
Math Connects, Course 2
261
Score:________/________
15-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
11-4
(over Lesson 11-3)
Solve.
For 1–2 find the circumference of each circle.
Use 3.14 for π. Round to the nearest tenth if
necessary.
1. radius = 5 ft
2. diameter = 11.2 in.
For Exercises 3–4 find the diameter or radius
of each circle. Use 3.14 for π. Round to the
nearest tenth if necessary.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. C = 30 ft, diameter = _____ ft
4. C = 96 cm, diameter = _____ cm
5.
A coffee can has a circumference
of 216 mm. Which equation could be used to find
the diameter of the can in inches?
Test Practice
A 216 = π d
C 108 = π × d
B C = π × 108
D C = π × 14.7
ANSWERS
1. 31.4 ft
2. 35.2 in
3. 9.6
Chapter 11
4. 30.6
5. A
Glencoe Math Connects, Course 2
11–4
Area of Circles
GLE: ME:1B,2C,2E
EXAMPLES
MAIN IDEA
• Find the areas of circles.
KEY CONCEPT
Area of a Circle The area
A of a circle equals the
product of pi (π) and the
square of its radius r.
Find the Areas of Circles
Find the area of the circle at the right.
A=
Area of a circle
A=π·
Replace r with
π
2
4 cm
.
x 2 ENTER
The area of the circle is approximately
centimeters.
square
KOI Find the area of the koi pond shown.
ÊΰÈʓ
The diameter of the pond is 3.6 meters, so the
1
radius is _
(3.6) or 1.8 meters.
2
A = πr
2
(
A=π
)
2
Replace r with
.
Use a calculator.
The area is approximately 10.2 square meters.
Check Your Progress
a. Find the area of the circle below.
10.5 ft
b. COINS Find the area of a nickel with a diameter of
2.1 centimeters.
262
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A≈
Area of a circle
11–4
BUILD YOUR VOCABULARY (pages 255–256)
A sector of a circle is a region of a circle bounded by
radii.
EXAMPLE
TEST EXAMPLE Mr. McGowan made an apple pie with a
diameter of 10 inches. He cut the pie into 6 equal slices.
Find the approximate area of each slice.
A 3 in 2
B 13 in 2
C 16 in 2
D 52 in 2
Read the Item
You can use the diameter to find the total area of the pie and
then divide that result by 6 to find the area of each slice.
Solve the Item
Find the area of the whole pie.
A = πr 2
A=π
( )
Area of a circle
2
A ≈ 78
Replace r with
.
Multiply.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the area of one slice.
HOMEWORK
ASSIGNMENT
78 ÷
= 13
The area of each slice is approximately 13 square inches.
The correct answer is
.
Check Your Progress MULTIPLE CHOICE The floor of
a merry-go-round at the amusement park has a diameter of 40
feet. The floor is divided evenly into eight sections, each having
a different color. Find the area of each section of the floor.
F 15.7 ft 2
H 62.8 ft 2
G 20 ft 2
J 157 ft 2
Page(s):
Exercises:
Math Connects, Course 2
263
Score:________/________
15-Square Answer Sheet-----MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
11-5
(over Lesson 11-4)
Find the area of each circle. Round to the
nearest tenth.
1.
2.
3.
4 ft
2.8 cm
13 m
3
4. diameter = 17ᎏᎏ yd
4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Find the area of the shaded
region in the figure at the right.
Round to the nearest tenth.
6 in.
12 in.
6.
What is the radius of a circle that
has an area of 154 square millimeters?
Test Practice
A 49 mm
C 8 mm
B 25 mm
D 7 mm
ANSWERS
1. 24.6 cm2
4. 247.4 yd2
Chapter 11
2. 50.3 ft2
5. 84.8 in2
3. 132.7 m2
6. D
Glencoe Math Connects, Course 2
11–6
Area of Composite Figures
GLE: ME:1B,2E
BUILD YOUR VOCABULARY (pages 255–256)
MAIN IDEA
A composite figure is made of triangles, quadrilaterals,
• Find the areas of
composite figures.
semicircles, and other
figures.
of a circle.
A semicircle is
EXAMPLE
Find the Area of a Composite Figure
Find the area of the figure in square centimeters.
The figure can be separated
into a
£{ÊV“
and a
. Find the area
£xÊV“
xÊV“
of each.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
®
ORGANIZE IT
In the tab for Lesson 11-6
of your Foldable, record
in words and symbols
how you find the area of
composite figures. Make
up an example of your
own and explain how
you would find the area.
£äÊV“
Area of Rectangle
Area of Triangle
A = w
1
A=_
bh
A = 15 · 10 or
1
A=_
(5)(4) or
2
2
The area is 150 + 10 or
square centimeters.
Check Your Progress Find the area of the figure shown.
Ê£xÊÞ`
ÇÊÞ`
Ê£™ÊÞ`
Math Connects, Course 2
265
11–6
WRITE IT
Explain in general terms
how to subdivide a
composite figure so you
can find its area.
EXAMPLE
Find the Area of a Composite Figure
WINDOWS The diagram at the right
shows the dimensions of a window.
Find the area of the window. Round
to the nearest tenth.
Ç°ÓÊvÌ
The figure can be separated into a semicircle
and a rectangle.
Area of Semicircle
ΰ{ÊvÌ
πr 2
A=
Area of a semicircle
1
π
A=_
Replace r with
A≈
Simplify.
2
÷
or
-
or
.
Area of Rectangle
A = w
Area of a rectangle
A=
Replace with
and w with
Multiply.
The area of the window is approximately
+
or
square feet.
Check Your Progress The diagram below shows the
dimensions of a new driveway. Find the area of the driveway.
Round to the nearest tenth.
21 ft
9 ft
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
266
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A=
.
Score:________/________
10-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
11-7
(over Lesson 11-6)
Find the area of each figure. Round to the
nearest tenth if necessary.
1.
2.2 yd
2.
12 in.
2 in.
6 yd
5 in.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9 in.
3. India wants to carpet her bedroom and closet.
If her bedroom is 10.5 feet by 11 feet and her
closet is 4.5 feet by 3 feet, how much area does
she need to carpet?
4.
Find the
area of the figure at
the right.
14 ft
Test Practice
12 ft
5 ft
22 ft
A 374 square feet
C 264 square feet
B 278 square feet
D 208 square feet
ANSWERS
1. 27.3 yd2
3. 129 ft2
Chapter 11
2. 58.5 in2
4. D
Glencoe Math Connects, Course 2
11–7
Three-Dimensional Figures
GLE: GR:4A,4B
BUILD YOUR VOCABULARY (pages 255–256)
MAIN IDEA
A three-dimensional figure has length, width, and depth.
• Classify threedimensional figures.
A face is a flat
. The edges are the segments
. The edges
formed by intersecting
at the vertices. The
are called
lateral faces.
EXAMPLES
Classify Three-Dimensional Figures
For each figure, identify the shape of the base(s). Then
classify the figure.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
®
ORGANIZE IT
Record notes about
classifying threedimensional figures
under the tab for
Lesson 11-7 of your
Foldable.
The figure has four
triangular faces and
one rectangular base.
The figure is a
The base and all other
faces are rectangles.
The figure is a
.
.
Check Your Progress For each figure, identify the
shape of the base(s). Then classify the figure.
a.
b.
Math Connects, Course 2
267
11–7
BUILD YOUR VOCABULARY (pages 255–256)
The top and bottom faces of a three-dimensional figure are
called the bases.
A prism has at least three lateral faces that are rectangles.
A pyramid has at least three lateral faces that are triangles.
A cone has one base that is a
A cylinder has two bases that are
and one vertex.
circles.
All of the points on a sphere are the same distance from
the center.
EXAMPLE
HOUSES Classify the shape of the house’s roof as a
three-dimensional figure.
REMEMBER IT
The base tells the
name of the threedimensional figure.
The shape of the house’s roof
is a
.
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
268
Math Connects, Course 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Your Progress Classify the shape of the house
above, not including the roof.
Score:________/________
10-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
5-Minute Check
Use with Lesson
(over Lesson 11-7)
11-8
For each figure, identify the shape of the
base(s). Then classify the figure.
1.
2.
3.
4.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5.
Which
figure is shown?
Test Practice
A pentagonal prism
B triangular prism
C pentagonal prism
D pentagonal pyramid
ANSWERS
1. rectangular prism
2. pentagonal prism
3. cylinder
4. rectangular pyramid
5. D
Chapter 11
Glencoe Math Connects, Course 2
11–8
Drawing Three-Dimensional Figures
GLE: GR:1A,4A,4B
EXAMPLE
MAIN IDEA
• Draw a threedimensional figure
given the top, side, and
front views.
Draw a Three-Dimensional Figure
Draw a top, a side, and a front view of the figure below.
The top and front views are
view is a
. The side
.
®
ORGANIZE IT
Record notes about
drawing threedimensional figures
under the tab for
Lesson 11-8 in your
Foldable. Sketch
examples of rectangular
prisms and cylinders.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
̜«
È`i
vÀœ˜Ì
Check Your Progress Draw a top, a side, and a front view
of the figure below.
Math Connects, Course 2
269
11–8
EXAMPLE
REMEMBER IT
There is more than
one way to draw the
different views of a
three-dimensional figure.
Draw a Three-Dimensional Figure
Draw the three-dimensional figure whose top, side, and
front views are shown below. Use isometric dot paper.
È`i
̜«
vÀœ˜Ì
Step 1
Use the top view to draw the base of the figure.
Step 2
Add edges to make the base a solid figure.
Step 3
Use the side and front views to complete the figure.
TOP
SIDE
FRONT
Check Your Progress Draw a solid using the top, side, and
front views shown below. Use isometric dot paper.
̜«
Page(s):
Exercises:
270
Math Connects, Course 2
vÀœ˜Ì
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
HOMEWORK
ASSIGNMENT
È`i
Use with Lesson
5-Minute Check
11-9
(over Lesson 11-8)
Draw a top, a side, and a front view of the
solid.
1.
Draw the solid using the top, side, and front
views shown. Use isometric dot paper.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2.
3.
top
side
front
What is the side
view of the figure at the right?
Test Practice
A rectangle
C triangle
B square
D parallelogram
ANSWERS·
1. top
side
Chapter 11
front
2.
3. C
Glencoe Math Connects, Course 2
Volume of Prisms
11–9
GLE: ME:1A,1B,2C,2E
BUILD YOUR VOCABULARY (pages 255–256)
MAIN IDEA
A volume of a three-dimensional figure is the measure of
• Find the volumes
of rectangular and
triangular prisms.
occupied by it.
A rectangular prism is a prism that has rectangular
. A triangular prism has
EXAMPLE
bases.
Volume of a Rectangular Prism
Find the volume of the rectangular prism.
ÓÊV“
ÎÊV“
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
{ÊV“
KEY CONCEPT
Volume of a Rectangular
Prism The volume V of a
rectangular prism is the
area of the base B times
the height h. It is also the
product of the length
, the width w, and the
height h.
V = wh
Volume of a
V=
Replace with
and h with
V=
The volume is 24
, w with
,
.
Multiply.
centimeters.
Check Your Progress Find the volume of the
rectangular prism.
HOMEWORK
ASSIGNMENT
Èʈ˜°
Page(s):
Exercises:
{ʈ˜°
£äʈ˜°
Math Connects, Course 2
271
Score:________/________
20-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________
Use with Lesson
5-Minute Check
11-10
(over Lesson 11-9)
Find the volume of each rectangular prism.
Round to the nearest tenth if necessary.
1.
2.
6 in.
5 in.
11 in.
3.4 cm
10 cm
3.4 cm
Solve.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. A cube has 6-inch edges. Find its volume.
4. Kieran’s greenhouse is 25 feet long, 13 feet wide,
and 14 feet high. She needs to know how many
humidifiers to buy for the greenhouse. If each
humidifier serves 1,000 ft3, how many
humidifiers should she buy?
5.
What is the volume of a closet
that is 6 feet wide, 4 feet deep, and 10 feet tall?
Test Practice
A 24 ft3
ANSWERS
1. 330 in3
2. 115.6 cm3
Chapter 11
B 60 ft3
C 154 ft3
3. 216 in3
4. 5
D 240 ft3
5. D
Glencoe Math Connects, Course 2
11–10
Volume of Cylinders
GLE: ME:1A,1B,2C,2E
EXAMPLE
MAIN IDEA
• Find the volumes of
Find the Volume of a Cylinder
Find the volume of the cylinder. Round to the nearest
tenth.
x°xÊV“
cylinders.
™ÊV“
V=
Volume of a cylinder
V=π
Replace the variables.
V≈
Use 3.14 for π.
The volume is about
cubic centimeters.
KEY CONCEPT
Check Your Progress Find the volume of the cylinder.
Round to the nearest tenth.
®
Take notes on
how to find the volume
of cylinders under the tab
for Lesson 11-10 of your
Foldable.
272
Math Connects, Course 2
Èʈ˜°
£{°xʈ˜°
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Volume of a Cylinder The
volume V of a cylinder
with radius r is the area
of the base B times the
height h.
11–10
EXAMPLE
COFFEE How much coffee can the can hold?
&INEST
#OFFEE
Èʈ˜°
ÊÎʈ˜°
V = πr 2h
WRITE IT
Explain how you would
use a calculator to
evaluate a power.
(
V=π
V≈
Volume of a cylinder
)
2
Replace r with
and h with
.
Simplify.
The coffee can holds about
cubic inches.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Check Your Progress JUICE Find the volume of a
cylinder-shaped juice can that has a diameter of 5 inches
and a height of 8 inches.
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
Math Connects, Course 2
273
Score:________/________
20-Square Answer Sheet------MAKE SURE YOU SHOW ALL YOUR WORK!
Name____________________________________________
Date ____________________________________________
Hour_____________________________________________
Lesson_____________________
#s_________________________
___________________________