# Splash Screen. Lesson Menu Five-Minute Check (over Lesson 12–2) CCSS Then/Now New Vocabulary Key Concept: Lateral Area of a Regular Pyramid Example 1:Lateral.

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Lesson Menu Five-Minute Check (over Lesson 12–2) CCSS Then/Now 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

Over Lesson 12–2 5-Minute Check 1 A.65.3 ft 2 B.80.2 ft 2 C.122.5 ft 2 D.130.7 ft 2 Find the lateral area of the cylinder.

Over Lesson 12–2 5-Minute Check 1 A.65.3 ft 2 B.80.2 ft 2 C.122.5 ft 2 D.130.7 ft 2 Find the lateral area of the cylinder.

Over Lesson 12–2 5-Minute Check 2 A.150 in 2 B.126 in 2 C.108 in 2 D.96 in 2 Find the lateral area of the prism.

Over Lesson 12–2 5-Minute Check 2 A.150 in 2 B.126 in 2 C.108 in 2 D.96 in 2 Find the lateral area of the prism.

Over Lesson 12–2 5-Minute Check 3 A.320 mm 2 B.400 mm 2 C.494.2 mm 2 D.502 mm 2 Find the surface area of the prism.

Over Lesson 12–2 5-Minute Check 3 A.320 mm 2 B.400 mm 2 C.494.2 mm 2 D.502 mm 2 Find the surface area of the prism.

Over Lesson 12–2 5-Minute Check 4 A.962.5 cm 2 B.1005.3 cm 2 C.1243.6 cm 2 D.1407.4 cm 2 Find the surface area of the cylinder.

Over Lesson 12–2 5-Minute Check 4 A.962.5 cm 2 B.1005.3 cm 2 C.1243.6 cm 2 D.1407.4 cm 2 Find the surface area of the cylinder.

Over Lesson 12–2 5-Minute Check 5 A.426 m 2 B.451 m 2 C.501 m 2 D.526 m 2 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?

Over Lesson 12–2 5-Minute Check 5 A.426 m 2 B.451 m 2 C.501 m 2 D.526 m 2 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?

CCSS Content Standards G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Mathematical Practices 1 Make sense of problems and persevere in solving them. 6 Attend to precision.

Then/Now You found areas of regular polygons. Find lateral areas and surface areas of pyramids. Find lateral areas and surface areas of cones.

Vocabulary regular pyramid slant height right cone oblique cone

Concept

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:

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.

Example 1 A.54 in 2 B.64 in 2 C.108 in 2 D.132 in 2 Find the lateral area of the square pyramid.

Example 1 A.54 in 2 B.64 in 2 C.108 in 2 D.132 in 2 Find the lateral area of the square pyramid.

Concept

Example 2 Surface Area of a Square Pyramid Find the surface area of the square pyramid to the nearest tenth. Step 1Find the slant height c 2 = a 2 + b 2 Pythagorean Theorem ℓ 2 = 6 2 + 4 2 a = 6, b = 4, and c = ℓ ℓ= Simplify.

Example 2 Surface Area of a Square Pyramid Answer: Step 2Find the perimeter and area of the base. P= 4 ● 8 or 32 mA = 8 2 or 64 m 2 Step 3Find the surface area of the pyramid. S= Pℓ + BSurface area of a regular pyramid __ 1 2 1 2 = (32) + 64P = 32, ℓ =, B = 64 ≈ 179.4Use a calculator.

Example 2 Surface Area of a Square Pyramid Answer:The surface area of the pyramid is about 179.4 square meters. Step 2Find the perimeter and area of the base. P= 4 ● 8 or 32 mA = 8 2 or 64 m 2 Step 3Find the surface area of the pyramid. S= Pℓ + BSurface area of a regular pyramid __ 1 2 1 2 = (32) + 64P = 32, ℓ =, B = 64 ≈ 179.4Use a calculator.

Example 2 A.96 in 2 B.124.3 in 2 C.138.5 in 2 D.156 in 2 Find the surface area of the square pyramid to the nearest tenth.

Example 2 A.96 in 2 B.124.3 in 2 C.138.5 in 2 D.156 in 2 Find the surface area of the square pyramid to the nearest tenth.

Example 3 Surface Area of a Regular Pyramid Step 1Find the perimeter of the base. P = 6 ● 10.4 or 62.4 cm Find the surface area of the regular pyramid. Round to the nearest tenth.

Example 3 Surface Area of a Regular Pyramid Step 2Find the length of the apothem and the area of the base. A central angle of the hexagon is or 60°, so the angle formed in the triangle is 30°. ______ 360° 6

Example 3 Surface Area of a Regular Pyramid tan 30° =Write a trigonometric ratio to find the apothem a. a= Solve for a. a≈ 9.0Use a calculator. A= Pa Area of a regular polygon ≈ (62.4)(9.0)Replace P with 62.4 and a width 9.0. ≈ 280.8Multiply. So, the area of the base is approximately 280.8 cm 2.

Example 3 Surface Area of a Regular Pyramid Answer: Step 3Find the surface area of the pyramid. S= Pℓ + B Surface area of regular pyramid ≈ (62.4)(15) + 280.8P = 62.4, ℓ = 15, and B ≈ 280.8 ≈ 748.8Simplify.

Example 3 Surface Area of a Regular Pyramid Answer: The surface area of the pyramid is about 748.8 cm 2. Step 3Find the surface area of the pyramid. S= Pℓ + B Surface area of regular pyramid ≈ (62.4)(15) + 280.8P = 62.4, ℓ = 15, and B ≈ 280.8 ≈ 748.8Simplify.

Example 3 A.198 in 2 B.228.5 in 2 C.255.5 in 2 D.316.3 in 2 Find the surface area of the regular pyramid. Round to the nearest tenth.

Example 3 A.198 in 2 B.228.5 in 2 C.255.5 in 2 D.316.3 in 2 Find the surface area of the regular pyramid. Round to the nearest tenth.

Concept

Example 4 Lateral Area of a Cone ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of inches. Find the lateral area of the sugar cone. If the cone has a diameter of then the radius Use the altitude and the radius to find the slant height with the Pythagorean Theorem.

Example 4 Lateral Area of a Cone Step 1Find the slant height ℓ. ℓ 2 =8 2 + 1.25 2 Pythagorean Theorem ℓ 2 ≈65.56Simplify. ℓ≈8.1Take the square root of each side. Step 2Find 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:

Example 4 Lateral Area of a Cone Step 1Find the slant height ℓ. ℓ 2 =8 2 + 1.25 2 Pythagorean Theorem ℓ 2 ≈65.56Simplify. ℓ≈8.1Take the square root of each side. Step 2Find 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.

Example 4 A.39.7 in. 2 B.43.6 in. 2 C.48.2 in. 2 D.53.1 in. 2 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.

Example 4 A.39.7 in. 2 B.43.6 in. 2 C.48.2 in. 2 D.53.1 in. 2 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.

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 cm 2 S=  rℓ +  r 2 Surface area of a cone =  (1.4)(3.2) +  (1.4) 2 r = 1.4 and ℓ = 3.2 ≈20.2 Answer:

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 cm 2 S=  rℓ +  r 2 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.

Example 5 A.58.2 cm 2 B.61.3 cm 2 C.63.6 cm 2 D.70.7 cm 2 Find the surface area of the cone. Round to the nearest tenth.

Example 5 A.58.2 cm 2 B.61.3 cm 2 C.63.6 cm 2 D.70.7 cm 2 Find the surface area of the cone. Round to the nearest tenth.

Concept

End of the Lesson

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