Transcript 12.4

Five-Minute Check (over Lesson 12–3)
Main Idea and Vocabulary
Key Concept: Surface Area of a Rectangular Prism
Example 1: Find Surface Area
Example 2: Find Surface Area
Example 3: Real-World Example
Example 4: Use the Pythagorean Theorem
• Find the surface areas of rectangular prisms.
• surface area
Find Surface Area
Find the surface area of the rectangular prism.
You can use a net of the
rectangular prism to find its
surface area. There are
three pairs of congruent
faces.
•
top and bottom
•
front and back
•
two sides
Find Surface Area
Faces
Area
top and bottom
2(6 ● 2) = 24
front and back
2(6 ● 3) = 36
two sides
2(2 ● 3) = 12
sum of the areas 24 + 36 + 12 = 72
Answer: The surface area is 72 square centimeters.
Find the surface area of the
rectangular prism.
A. 16 ft2
B. 108 ft2
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D. 162 ft
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C. 150 ft
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Find Surface Area
Find the surface area of the
rectangular prism.
Replace ℓ with 10, w with 8, and
h with 12.
surface area = 2ℓw + 2ℓh + 2wh
= 2 ●10 ● 8 + 2 ● 10 ● 12 + 2 ● 8 ● 12
= 160 + 240 + 192
= 592
Answer: 592 in2
Multiply first.
Then add.
Find the surface area of the rectangular prism.
A. 22 cm2
B. 210 cm2
C. 254 cm2
D. 312 cm
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BOXES Drew is putting together a cardboard box
that is 9 inches long, 6 inches wide, and 8 inches
high. He bought a roll of wrapping paper that is 1
foot wide and 3 feet long. Did he buy enough to
wrap the box? Justify your answer.
Step 1
Find the surface area of the box.
Replace ℓ with 9, w with 6, and h with 8.
surface area = 2ℓw + 2ℓh + 2wh
=2●9●6+2●9●8+2●6●8
= 348 in2
Step 2
Find the area of the wrapping paper.
1 ft
3 ft
area = 12 in. ● 36 in. or 432 in2
Answer: Since 348 in2 < 432 in2, Drew bought enough
paper.
A. yes; 360 > 310
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B. yes; 328 > 295
C. no; 360 < 412
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D. no; 310 < 360
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Use the Pythagorean Theorem
Find the surface area of the rectangular prism.
The width and length of the prism are given. To find
surface area, you need to find the height of the prism.
Notice that the diagonal, length, and height of the front
face of the prism form a right triangle.
Use the Pythagorean Theorem
c2 = a2 + b2
Pythagorean Theorem
72 = 32 + b2
Replace c with 7 and a with 3.
49 = 9 + b2
Evalute powers.
49 – 9 = 9 + b2 – 9 Subtract 9 from each side.
40 = b2
Simplify.
Definition of square root
±6.3 = b
Simplify.
The height of the prism is 6.3 meters. Find the surface
area.
Use the Pythagorean Theorem
surface area = 2ℓw + 2ℓh + 2wh
= 2 • 3 • 5 + 2 • 3 • 6.3 + 2 • 5 • 6.3
= 30 + 37.8 + 63
Multiply first. Then add.
= 130.8
Answer: The surface area of the prism is 130.8 square
meters.
Find the surface area of a
rectangular prism that has
width 5 feet, diagonal 13 feet,
and height 2 feet.
A. 188 square feet
B. 215 square feet
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C. 241 square feet
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D. 256 square feet
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End of the Lesson
Five-Minute Check (over Lesson 12–3)
Image Bank
Math Tools
The Pythagorean Theorem
(over Lesson 12-3)
Solve the problem by making a model.
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(over Lesson 12-3)
Solve the problem by making a model.
A sports collector shop arranges four of its most
expensive baseball cards in the top display case
four in a row. In how many different ways can four
baseball cards be arranged in a row?
A. 16
B. 12
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C. 20
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D. 24
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(over Lesson 12-3)
Solve the problem by making a model.
Helen wrote checks for $26.75, $134, and $52. If she
now has $82.50 in her checking account, how much
did she have to begin with?
A. $130.25
B. $563
D. $212.75
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C. $295.25
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(over Lesson 12-3)
Mr. Green has a square flowerbed that is 8 feet long
on each side. He puts a stone border around it that
is 1 foot wide. What is the perimeter of the stone
border?
A. 81 ft
B. 64 ft
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C. 40 ft
D. 34 ft
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