# 12-4: Surface Areas of Pyramids and Cones

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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 l = slant height l

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

12-4: Surface Area of Pyramids & Cones
Find the lateral area and surface area of the regular pentagon pyramid below L = ½Pl S = ½Pl + B What is the Perimeter of the base? 6cm • 5 = 30 cm What is the slant height? 11 cm What is the lateral area? ½ (30)(11) = 165 cm2 What is the area of the base? B = ½Pa = ½(30)(5.2) = 78 cm2 Put it all together for the surface area: S = ½(30)(11) + (78) = 243 cm2 11 cm 6 cm 5.2 cm

12-4: Surface Area of Pyramids & Cones
Find the lateral area and surface area of the regular pyramids below Lateral Area: 160 in2 Lateral Area: 70 m2 Surface Area: 224 in2 Surface Area: 98 m2

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

12-4: Surface Area of Pyramids & Cones
Surface Area of a Cone S = πrl + πr2, where: r = radius l = slant height (note: do not confuse this with height)

12-4: Surface Area of Pyramids & Cones
Find the lateral area and surface area of the cone to the right L = πrl S = πrl + πr2 What is the radius? 10 ft / 2 = 5 ft What is the slant height? Use Pythagorean Theorem: = x2 l = 13 What is the lateral area? (5)(13)  ft2 What is the surface area S = π(5)(13) + π(5)2 = 90π ≈ ft2 12 ft 10 ft

12-4: Surface Area of Pyramids & Cones
Find the lateral area and surface area of each cone below Lateral Area: m2 Lateral Area: in2 Surface Area: m2 Surface Area: in2

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