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12-4: Surface Areas of Pyramids and Cones

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12-4: Surface Area of Pyramids & Cones Lateral Area of a Pyramid ▫L = ½Pl, where P = Perimeter of the base l = slant height l

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12-4: Surface Area of Pyramids & Cones Surface Area of a Pyramid ▫S = ½Pl + B, where P = Perimeter of the base l = slant height B = area of the base l

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12-4: Surface Area of Pyramids & Cones Find the lateral area and surface area of the regular pentagon pyramid below ▫L▫L = ½PlS = ½Pl + B ▫W▫What is the Perimeter of the base? 6cm 5 = 30 cm ▫W▫What is the slant height? 111 cm ▫W▫What is the lateral area? ½½ (30)(11) = 165 cm 2 ▫W▫What is the area of the base? BB = ½Pa = ½(30)(5.2) = 78 cm 2 ▫P▫Put it all together for the surface area: SS = ½(30)(11) + (78) = 243 cm 2 5.2 cm 11 cm 6 cm

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12-4: Surface Area of Pyramids & Cones Find the lateral area and surface area of the regular pyramids below Lateral Area: 160 in 2 Surface Area: 224 in 2 Lateral Area: 70 m 2 Surface Area: 98 m 2

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12-4: Surface Area of Pyramids & Cones Lateral Area of a Cone ▫L = π rl, where: r = radius l = slant height (note: do not confuse this with height)

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12-4: Surface Area of Pyramids & Cones Surface Area of a Cone ▫S = π rl + π r 2, where: r = radius l = slant height (note: do not confuse this with height)

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12-4: Surface Area of Pyramids & Cones Find the lateral area and surface area of the cone to the right ▫L▫L = π rlS = π rl + π r 2 ▫W▫What is the radius? 110 ft / 2 = 5 ft ▫W▫What is the slant height? UUse Pythagorean Theorem: 5 2 + 12 2 = x 2 ll = 13 ▫W▫What is the lateral area? (5)(13) 204.20 ft 2 ▫W▫What is the surface area SS = π (5)(13) + π (5) 2 = 90 π ≈ 282.74 ft 2 10 ft 12 ft

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12-4: Surface Area of Pyramids & Cones Find the lateral area and surface area of each cone below Lateral Area: 113.10 m 2 Surface Area: 163.36 m 2 Lateral Area: 188.50 in 2 Surface Area: 301.59 in 2

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12-4: Surface Area of Pyramids & Cones Assignment ▫Worksheet #12-4

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