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12-4: Surface Areas of Pyramids and Cones. 12-4: Surface Area of Pyramids & Cones Lateral Area of a Pyramid ▫L = ½Pl, where  P = Perimeter of the base.

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Presentation on theme: "12-4: Surface Areas of Pyramids and Cones. 12-4: Surface Area of Pyramids & Cones Lateral Area of a Pyramid ▫L = ½Pl, where  P = Perimeter of the base."— Presentation transcript:

1 12-4: Surface Areas of Pyramids and Cones

2 12-4: Surface Area of Pyramids & Cones Lateral Area of a Pyramid ▫L = ½Pl, where  P = Perimeter of the base  l = slant height l

3 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

4 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? 111 cm ▫W▫What is the lateral area? ½½ (30)(11) = 165 cm 2 ▫W▫What is the area of the base? BB = ½Pa = ½(30)(5.2) = 78 cm 2 ▫P▫Put it all together for the surface area: SS = ½(30)(11) + (78) = 243 cm cm 11 cm 6 cm

5 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

6 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)

7 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)

8 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? 110 ft / 2 = 5 ft ▫W▫What is the slant height? UUse Pythagorean Theorem: = x 2 ll = 13 ▫W▫What is the lateral area?  (5)(13)  ft 2 ▫W▫What is the surface area SS = π (5)(13) + π (5) 2 = 90 π ≈ ft 2 10 ft 12 ft

9 12-4: Surface Area of Pyramids & Cones Find the lateral area and surface area of each cone below Lateral Area: m 2 Surface Area: m 2 Lateral Area: in 2 Surface Area: in 2

10 12-4: Surface Area of Pyramids & Cones Assignment ▫Worksheet #12-4


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