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Lesson Menu
Five-Minute Check (over Lesson 122) NGSSS Then/No
w New Vocabulary Key Concept Lateral Area of a
Regular Pyramid Example 1 Lateral Area of a
Regular Pyramid Key Concept Surface Area of a
Regular Pyramid Example 2 Surface Area of a
Square Pyramid Example 3 Surface Area of a
Regular Pyramid Key Concept Lateral and Surface
Area of a Cone Example 4 Real-World Example
Lateral Area of a Cone Example 5 Surface Area
of a Cone Concept Summary Lateral and Surface
Areas of Solids
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5-Minute Check 1
Find the lateral area of the cylinder.
A. 65.3 ft2 B. 80.2 ft2 C. 122.5 ft2 D. 130.6 ft2

1. A
2. B
3. C
4. D

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5-Minute Check 2
Find the lateral area of the prism.
A. 150 in2 B. 126 in2 C. 108 in2 D. 96 in2

1. A
2. B
3. C
4. D

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5-Minute Check 3
Find the surface area of the prism.
A. 320 mm2 B. 400 mm2 C. 494.2 mm2 D. 502 mm2

1. A
2. B
3. C
4. D

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5-Minute Check 4
Find the surface area of the cylinder.
A. 962.5 cm2 B. 1005.3 cm2 C. 1243.6
cm2 D. 1407.4 cm2

1. A
2. B
3. C
4. D

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5-Minute Check 5
The lateral area of a prism is 476 square meters.
The area of one of its bases is 25 square meters.
What is the surface area of the prism?
A. 426 m2 B. 451 m2 C. 501 m2 D. 526 m2

1. A
2. B
3. C
4. D

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NGSSS
MA.912.G.7.5 Explain and use formulas for lateral
area, surface area, and volume of solids.
MA.912.G.7.7 Determine how changes in dimensions
affect the surface area and volume of common
geometric solids. Also MA.912.G.7.2.
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Then/Now
You found areas of regular polygons.(Lesson 113)

• Find lateral areas and surface areas of pyramids.

• Find lateral areas and surface areas of cones.

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Vocabulary

• regular pyramid
• slant height
• right cone
• oblique cone

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Concept
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Example 1
Lateral Area of a Regular Pyramid
Find the lateral area of the square pyramid.
Lateral area of a regular pyramid
P 2.5 ? 4 or 10, l 5
Answer The lateral area is 25 square centimeters.
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Example 1
Find the lateral area of the square pyramid.
A. 54 in2 B. 64 in2 C. 108 in2 D. 132 in2

1. A
2. B
3. C
4. D

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Concept
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Example 2
Surface Area of a Square Pyramid
Find the surface area of the square pyramid to
the nearest tenth.
Step 1 Find the slant height c2 a2
b2 Pythagorean Theorem l2 62 42 a 6, b
4, and c l
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Example 2
Surface Area of a Square Pyramid
Step 2 Find the perimeter and area of the
base. P 4 ? 8 or 32 m A 82 or 64 m2 Step
3 Find the surface area of the pyramid.
179.4 Use a calculator.
Answer The surface area of the pyramid is about
179.4 square meters.
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Example 2
Find the surface area of the square pyramid to
the nearest tenth.
A. 96 in2 B. 124.3 in2 C. 138.5 in2 D. 156 in2

1. A
2. B
3. C
4. D

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Example 3
Surface Area of a Regular Pyramid
Find the surface area of the regular pyramid.
Round to the nearest tenth.
Step 1 Find the perimeter of the base. P 6 ?
10 ? 4 or 62.4 cm
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Example 3
Surface Area of a Regular Pyramid
Step 2 Find the length of the apothem and the
area of the base.
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Example 3
Surface Area of a Regular Pyramid
a 9.0 Use a calculator.
281.0 Multiply. So, the area of the base is
approximately 281.0 cm2.
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Example 3
Surface Area of a Regular Pyramid
Step 3 Find the surface area of the pyramid.
749 Simplify.
Answer The surface area of the pyramid is about
749.0 cm2.
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Example 3
Find the surface area of the regular pyramid.
Round to the nearest tenth.
A. 198 in2 B. 228.5 in2 C. 255.5 in2 D. 316.3 in2

1. A
2. B
3. C
4. D

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Concept
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Example 4
Lateral Area of a Cone
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Example 4
Lateral Area of a Cone
Step 1 Find the slant height l.
l2 82 1.252 Pythagorean Theorem
l2 65.56 Simplify.
l 8.1 Take the square root of each side.
Step 2 Find the lateral area L.
L ?rl Lateral area of a cone ?(1.25)(8.1)
r 1.25 and l 8.1 31.8
Answer The lateral area of the sugar cone is
about 31.8 square inches.
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Example 4
HATS A conical birthday hat has an altitude of
6 inches and a diameter of 4 inches. Find the
lateral area of the birthday hat.
A. 39.7 in.2 B. 43.6 in.2 C. 48.2 in.2 D. 53.1
in.2

1. A
2. B
3. C
4. D

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Example 5
Surface Area of a Cone
Find the surface area of the cone. Round to the
nearest tenth.
Estimate S 3 ? 1.5 ? 3 3 ? 2 or 19.5 cm2
S ?rl ?r2 Surface area of a
cone ?(1.4)(3.2) ?(1.4)2 r 1.4 and l
3.2 20.2
Answer The surface area of the cone is about
20.2 square centimeters. This is close to the
estimate, so the answer is reasonable.
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Example 5
Find the surface area of the cone. Round to the
nearest tenth.
A. 58.2 cm2 B. 61.3 cm2 C. 63.6 cm2 D. 70.7 cm2

1. A
2. B
3. C
4. D

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Concept
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End of the Lesson