Chapter 11
Measurement: Perimeter, Area, and Volume
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Measurement: Perimeter, Area, and Volume
11
Lesson 11-1
Perimeter
Lesson 11-2
Area of Parallelograms
Lesson 11-3
Problem-Solving Strategy: Make a
Model
Lesson 11-4
Area of Triangles
Lesson 11-5
Problem-Solving Investigation:
Choose the Best Strategy
Lesson 11-6
Volume of Rectangular Prisms
Lesson 11-7
Surface Area of Rectangular Prisms
11-1
Perimeter
Five-Minute Check (over Chapter 10)
Main Idea and Vocabulary
California Standards
Key Concept: Perimeter of a Square
Key Concept: Perimeter of a Rectangle
Example 1
Example 2
11-1
Perimeter
• I will find the perimeters of squares and
rectangles.
• perimeter
11-1
Perimeter
Standard 5MG1.4 Differentiate between, and
use appropriate units of measures for twoand three-dimensional objects (i.e., find the
perimeter, area, volume).
11-1
Perimeter
11-1
Perimeter
11-1
Perimeter
The base of the Eiffel Tower is shaped like a square
with each side measuring 125 meters. What is the
perimeter of the base?
P = 4s
P = 4(125)
P = 500
Perimeter of a square
Replace s with 125.
Multiply.
Answer: The perimeter of the base of the Eiffel Tower
is 500 meters.
11-1
Perimeter
The park is shaped like a square with each side
measuring 100 yards. What is the perimeter of the
park?
A.
400 feet
B.
400 yards
C.
200 yards
D.
100 yards
11-1
Perimeter
Find the perimeter of the rectangle.
7m
4m
P = 2 + 2w
P = 2(7) + 2(4)
P = 14 + 8
Write the formula.
Replace with 7 and w with 4.
Multiply.
P = 22
Add.
Answer: The perimeter is 22 meters.
11-1
Perimeter
Find the perimeter of the rectangle.
A.
7 cm
B.
6 cm
3 cm
1 cm
C.
8 cm
D.
10 cm
11-2
Area of Parallelograms
Five-Minute Check (over Lesson 11-1)
Main Idea
California Standards
Key Concept: Area of a Parallelogram
Example 1
Example 2
Example 3
11-2
Area of Parallelograms
• I will find the areas of parallelograms.
• base
• height
11-2
Area of Parallelograms
Standard 5MG1.1 Derive and use the
formula for the area of a triangle and of a
parallelogram by comparing it with the formula
for the area of a rectangle.
Standard 5MG1.4 Differentiate between, and use
appropriate units of measures for two- and threedimensional objects.
11-2
Area of Parallelograms
11-2
Area of Parallelograms
Find the area of the
parallelogram.
The base is 3 and the
height is 10.
A = bh
A = 3 • 10
A = 30
Area of parallelogram
Replace b with 3 and h with 10.
Multiply.
Answer: The area is 30 square units or 30 units2.
11-2
Area of Parallelograms
Find the area of the parallelogram.
A.
35 units2
B.
28 units2
C.
49 units2
D.
64 units2
11-2
Area of Parallelograms
Find the area of
the parallelogram.
A = bh
A = 8.2 • 4.5
A = 36.9
Area of parallelogram
Replace b with 8.2 and h with 4.5.
Multiply.
Answer: The area is 36.9 square centimeters or
36.9 cm2.
11-2
Area of Parallelograms
Find the area of the parallelogram.
A. 68 mm2
B. 70 mm2
C. 68.64 mm2
D. 70.42 mm2
11-2
Area of Parallelograms
A particular area rug is
shaped like a
parallelogram. Estimate
the area of the floor it
will cover.
Estimate 6 1 is about 6 and 10 1 is about 11.
4
2
A = bh
Area of parallelogram
A = 11 • 6
Replace b with 11 and h with 6.
A = 66
Multiply.
Answer: The area of the rug is about 66 ft2.
11-2
Area of Parallelograms
A parking lot is shaped like a parallelogram.
Estimate the area of ground it will cover.
A.
7,000 sq. yds.
B.
7,200 sq. yds.
C.
7,140 sq. yds.
D.
7,080 sq. yds.
11-3
Problem-Solving Strategy: Make a Model
Five-Minute Check (over Lesson 11-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
11-3
Problem-Solving Strategy: Make a Model
• I will solve problems by making a model.
11-3
Problem-Solving Strategy: Make a Model
Standard 5MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to explain
mathematical reasoning.
Standard 5MG1.4 Differentiate between, and use
appropriate units of measures for two- and threedimensional objects.
11-3
Problem-Solving Strategy: Make a Model
While volunteering at the local
farm market, Julia was asked to
make a display for the oranges.
She needs to stack the oranges in
the shape of a square pyramid.
The base should have 100
oranges and one orange needs to be on top. There
are 400 oranges total. Are 400 oranges enough to
make a square pyramid with a base of 100
oranges?
11-3
Problem-Solving Strategy: Make a Model
Understand
What facts do you know?
• The oranges need to be in the shape of a square
pyramid with 100 oranges in the base and 1
orange on top.
• There are 400 oranges altogether.
What do you need to find?
• Are 400 oranges enough to make a square
pyramid with a base of 100 oranges?
11-3
Problem-Solving Strategy: Make a Model
Plan
Make a model using pennies to find the number of
oranges needed.
11-3
Problem-Solving Strategy: Make a Model
Solve
Begin with 100 pennies. For each consecutive
layer, place 1 penny where 4 meet.
bottom layer
second layer
third layer
fourth layer
100
81
64
49
11-3
Problem-Solving Strategy: Make a Model
Solve
Answer: By continuing this pattern, 100 + 81 + 64 + 49
+ 36 + 25 + 16 + 9 + 4 + 1 or 385 oranges will
be needed. Since 385 < 400, 400 oranges are
enough to make a square pyramid.
11-3
Problem-Solving Strategy: Make a Model
Check
Look back at the problem. 400 – 100 – 81 – 64 – 49 –
36 – 25 – 16 – 9 – 4 – 1 leaves 15 oranges.
11-4
Area of Triangles
Five-Minute Check (over Lesson 11-3)
Main Idea
California Standards
Key Concept: Area of a Triangle
Example 1
Example 2
Example 3
Area of Triangles
11-4
Area of Triangles
• I will find the areas of triangles.
11-4
Area of Triangles
Standard 5MG1.1 Derive and use the
formula for the area of a triangle and of a
parallelogram by comparing it with the formula
for the area of a rectangle.
Standard 5MG1.4 Differentiate between, and use
appropriate units of measures for two- and threedimensional objects.
11-4
Area of Triangles
11-4
Area of Triangles
Find the area of the
triangle.
By counting, you find that the
measure of the base of the
triangle is 5 and the height is 8.
A=
1
bh
2
1
A = (5) • (8)
2
Area of a triangle
Replace b with 5 and h with 8.
11-4
Area of Triangles
A=
1
(40)
2
A = 20
Multiply.
Multiply.
Answer: The area of the triangle is 20 square units.
11-4
Area of Triangles
Find the area of the triangle.
A. 25 sq. units
B. 16 sq. units
C. 12
1
sq. units
2
D. 20 sq. units
11-4
Area of Triangles
Find the area of
the triangle.
A=
1
bh
2
1
A = (16.4) • (7.9)
2
Area of a triangle
Replace b with 16.4 and h
with 7.9.
11-4
Area of Triangles
A=
1
(129.56)
2
A = 64.78
Multiply.
Divide. 129.56 ÷ 2 = 64.78
Answer: The area of the triangle is 64.78 square
meters.
11-4
Area of Triangles
Clio cut out a banner in the shape of a triangle.
What is the area of the banner?
A.
99 sq. cm
B.
99 cm
C.
49 1 cm
2
1
D. 49 sq. cm
2
11-4
Area of Triangles
Find the area of
the triangle.
A=
1
bh
2
1
A = (12) • (6)
2
Area of a triangle
Replace b with 12 and h with 6.
11-4
Area of Triangles
A=
1
(72)
2
A = 36.5
Multiply.
Divide. 72 ÷ 2 = 36.5
Answer: The area of the triangle is 36.5 square
inches.
11-4
Area of Triangles
Kira drew a triangle on the sidewalk with chalk.
What is the area of her triangle?
A.
21 sq. ft
B.
10.5 sq. ft
C.
20 sq. ft
D.
11 sq. ft
11-5
Problem-Solving Investigation: Choose the Best Strategy
Five-Minute Check (over Lesson 11-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
11-5
Problem-Solving Investigation: Choose the Best Strategy
• I will choose the best strategy to solve a problem.
11-5
Problem-Solving Investigation: Choose the Best Strategy
Standard 5MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to
explain mathematical reasoning.
Standard 5MG1.4 Differentiate between, and use
appropriate units of measures for two- and threedimensional objects.
11-5
Problem-Solving Investigation: Choose the Best Strategy
ROSS: I want people to find out
about a party I’m having, so I will
tell Jamie and Cara and have each
of them tell two friends, and so
on. I wonder how many people would
be invited to the party in three
minutes if two friends tell another
two friends each minute?
YOUR MISSION: Find the number of
people who would be invited to the
party in three minutes.
11-5
Problem-Solving Investigation: Choose the Best Strategy
Understand
What facts do you know?
• You know that Ross tells Jamie and Cara about
the party, and then each friend tells two other
friends each minute.
What do you need to find?
• You need to find the number of people who
would be invited to the party in three minutes.
11-5
Problem-Solving Investigation: Choose the Best Strategy
Plan
Draw a diagram to show the number of people
who would be invited to the party.
11-5
Problem-Solving Investigation: Choose the Best Strategy
Solve
Answer: So, 14 people would be invited to the party.
11-5
Problem-Solving Investigation: Choose the Best Strategy
Check
Look back at the problem to see if the diagram
meets all of the requirements. Since the diagram
is correct, the answer is correct.
11-6
Volume of Rectangular Prisms
Five-Minute Check (over Lesson 11-5)
Main Idea and Vocabulary
California Standards
Key Concept: Volume of a Rectangular Prism
Example 1
Example 2
11-6
Volume of Rectangular Prisms
• I will find the volume of rectangular prisms.
• rectangular prism
• volume
• cubic units
11-6
Volume of Rectangular Prisms
Standard 5MG1.3 Understand the concept
of volume and use the appropriate units in
common measuring systems to compute the
volume of rectangular solids.
Standard 5MG1.4 Differentiate between, and
use appropriate units of measures for two- and
three-dimensional objects (i.e., find the
perimeter, area, volume).
11-6
Volume of Rectangular Prisms
11-6
Volume of Rectangular Prisms
Find the volume of the
rectangular prism.
Estimate V ≈ 10 m × 10 m × 5 m or 500 m3
In the figure, the length is 10 meters, the width is 8
meters, and the height is 5 meters.
Use V = wh.
11-6
Volume of Rectangular Prisms
V = wh
Volume of rectangular prism
V = 10 • 8 • 5
Replace with 10, w with 8, and
h with 5.
V = 400
Multiply.
Answer: The volume is 400 cubic meters.
11-6
Volume of Rectangular Prisms
Check for Reasonableness
Since we overestimated, the answer should be
less than the estimate. 400 < 500.
11-6
Volume of Rectangular Prisms
Find the volume of a rectangular prism with a length
of 14 mm, a width of 6 mm, and a height of 3 mm.
A.
250 mm3
B.
300 mm3
C.
252 mm3
D.
254 mm3
11-6
Volume of Rectangular Prisms
A closet is 6.2 feet long, 2.8 feet wide, and 8.1 feet
high. Find the amount of space contained within
the closet for storage. Round to the nearest foot.
Estimate V ≈ 6 ft × 3 ft × 8 ft or 144 ft3
11-6
Volume of Rectangular Prisms
V=
wh
Volume of rectangular prism
V = 6.2 • 2.8 • 8.1
Replace with 6.2, w with 2.8,
and h with 8.1.
V = 140.686
Multiply, then round to the
nearest foot.
Answer: The storage space in the closet is
about 141 cubic feet.
11-6
Volume of Rectangular Prisms
Check for Reasonableness
Compare to the estimate. 141 ≈ 144.
11-6
Volume of Rectangular Prisms
A tissue box is 12 inches long, 5 inches wide and 5
inches high. Find the amount of space contained
within the box for tissues.
A.
300 cubic inches
B.
250 cubic inches
C.
125 cubic inches
D.
315 cubic inches
11-7
Surface Area of Rectangular Prisms
Five-Minute Check (over Lesson 11-6)
Main Idea and Vocabulary
California Standards
Key Concept: Surface Area of a Rectangular Prism
Example 1
Example 2
Using a Net to Build a Cube
11-7
Surface Area of Rectangular Prisms
• I will find the surface areas of rectangular prisms.
• surface area
11-7
Surface Area of Rectangular Prisms
Standard 5MG1.2 Construct a cube and
rectangular box from two-dimensional patterns
and use these patterns to compute the surface
area for these objects.
11-7
Surface Area of Rectangular Prisms
11-7
Surface Area of Rectangular Prisms
Find the surface area of the rectangular prism.
Find the area of each face.
top and bottom:
2( w) = 2(8 × 4) or 74
11-7
Surface Area of Rectangular Prisms
front and back:
2( h) = 2(8 × 3) or 48
two sides:
2(wh) = 2(4 × 3) or 24
Add to find the surface area.
Answer: The surface area is 74 + 48 + 24 or
136 square centimeters.
11-7
Surface Area of Rectangular Prisms
Find the area of a rectangular prism that is 12 in
long, 6 in wide, and 5 in high.
A.
320 square inches
B.
300 square inches
C.
324 square inches
D.
342 square inches
11-7
Surface Area of Rectangular Prisms
A box measures 13 inches long, 7 inches wide, and
4 inches deep. What is the surface area of the box?
S = 2 w + 2 h + 2wh
S = 2(13 × 7) + 2(13 × 4) + 2(7 × 4)
Surface area of a prism
= 13, w = 7, h = 4
S = 2(91) + 2(52) + 2(28)
Simplify within
parentheses.
S = 182 + 104 + 56
Multiply.
S = 342
Add.
Answer: The box has a surface area of 342 square inches.
11-7
Surface Area of Rectangular Prisms
A flat screen television measure 48 inches long,
2 inches wide, and 25 inches high. What is the
surface area of the TV?
A.
2,692 square inches
B.
2,700 square inches
C.
1,874 square inches
D.
2,962 square inches
Measurement: Perimeter, Area, and Volume
11
Five-Minute Checks
Area of Triangles
Using a Net to Build a Cube
Measurement: Perimeter, Area, and Volume
11
Lesson 11-1 (over Chapter 10)
Lesson 11-2 (over Lesson 11-1)
Lesson 11-3 (over Lesson 11-2)
Lesson 11-4 (over Lesson 11-3)
Lesson 11-5 (over Lesson 11-4)
Lesson 11-6 (over Lesson 11-5)
Lesson 11-7 (over Lesson 11-6)
Measurement: Perimeter, Area, and Volume
11
(over Chapter 10)
Draw the three-dimensional figure whose top,
side, and front views are shown. Use isometric
dot paper.
top
side
front
A.
B.
Measurement: Perimeter, Area, and Volume
11
(over Chapter 10)
Draw the three-dimensional figure whose top,
side, and front views are shown. Use isometric
dot paper.
top
side
front
C.
D.
Measurement: Perimeter, Area, and Volume
11
(over Chapter 10)
Draw the three-dimensional figure whose top,
side, and front views are shown. Use isometric
dot paper.
B.
Measurement: Perimeter, Area, and Volume
11
(over Chapter 10)
Draw the three-dimensional figure whose top, side,
and front views are shown. Use isometric dot paper.
top
A.
side
B.
front
Measurement: Perimeter, Area, and Volume
11
(over Chapter 10)
Draw the three-dimensional figure whose top, side,
and front views are shown. Use isometric dot paper.
top
C.
side
D.
front
Measurement: Perimeter, Area, and Volume
11
(over Chapter 10)
Draw the three-dimensional figure whose top, side,
and front views are shown. Use isometric dot paper.
C.
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-1)
Find the perimeter of each square or rectangle.
length 7 in, width 4 in
A. 11 in
B. 28 in
C. 3 in
D. 22 in
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-1)
Find the perimeter of each square or rectangle.
sides 13 cm
A. 52 cm
B. 25 in
C. 36 cm
D. 62 cm
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-1)
Find the perimeter of each square or rectangle.
length 14 ft, width 10 ft
A. 24 ft
B. 48 ft
C. 144 ft
D. 140 in
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-1)
Find the perimeter of each square or rectangle.
sides 25 yd
A. 100 yd
B. 25 yd
C. 255 ft
D. 125 ft
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-2)
Find the area of each parallelogram.
base 14 yd, height 8 yd
A. 128 yd2
B. 28 yd2
C. 248 yd2
D. 112 yd2
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-2)
Find the area of each parallelogram.
base 13 ft, height 11 ft
A. 143 ft2
B. 141 ft2
C. 144 ft2
D. 144 yd2
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-2)
Find the area of each parallelogram.
base 8 in, height 6
A. 48 in2
B. 44 in2
C. 52 in2
D. 48 ft
1
in
2
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-2)
Find the area of each parallelogram.
base 9.6 cm, height 5.2 cm
A. 49.92 cm2
B. 45.12 cm2
C. 14.8 cm2
D. 24.8 cm2
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-3)
Solve. Use the make a model strategy. Cans of tuna
are stacked into a 4-layer pyramid-shaped display.
The bottom layer is 8-cans long and 4-cans wide.
There is 1 less can in the length and width of each
layer above it. How many cans are on display?
A. 48 cans
B. 52 cans
C. 44 cans
D. 70 cans
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-4)
Find the area of each triangle.
base 5 ft, height 5 ft
A. 25 ft2
B. 25 ft
C. 12.5 ft2
D. 12.5 ft
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-4)
Find the area of each triangle.
base 48 cm, height 23 cm
A. 557 cm2
B. 71 cm2
C. 554 cm2
D. 600 cm2
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-4)
Find the area of each triangle.
base 5.2 cm, height 3.2 cm
A. 2.32 cm2
B. 8.32 cm2
C. 15.23 cm2
D. 18.32 cm2
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-4)
Find the area of each triangle.
base 5 in, height 7 1 in
2
1
A. 12 in
2
1
B. 30 2 in
C. 2 in
3
D. 18 in
4
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-5)
Tell what strategy you used. Desta saved $1 the first
week. After that she saved $2 more each week than
she had the week before. How much money did she
save in the tenth week?
A. $22
B. $24
C. $19
D. $34
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-6)
Find the volume of each prism.
length 8 yd, width 7 yd, height 3 yd
A. 168 yd3
B. 18 yd3
C. 59 yd3
D. 88 yd3
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-6)
Find the volume of each prism.
length 12 cm, width 8 cm, height 5 cm
A. 240 cm3
B. 480 cm3
C. 144 in
D. 25 in
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-6)
Find the volume of each prism.
length 5
1
ft, width 3 ft, height 9 ft
4
A. 144 ft3
3 3
B. 141 ft
4
C. 3,444 in
D. 1,333 cm
Measurement: Perimeter, Area, and Volume
11
(over Lesson 11-6)
Find the volume of each prism.
length 2.4 cm, width 17.1 cm, height 3.6 cm
A. 156.222 cm3
B. 147.744 cm3
C. 24 cm3
D. 444 in
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