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6.3 Surface Area of Pyramids and Cones OBJECTIVE: Determine the surface areas and lateral areas of pyramids and cones. 1 6.3 Surface Area of Pyramids and Cones The vertex of a pyramid is the point opposite the base of the pyramid. The base of a regular pyramid is a regular polygon, and the lateral faces are congruent isosceles triangles. The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. 2 The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid. 3 r = radius B = area of base h = height of prism P = perimeter of base Surface Area S= L = S = L + 2B L = Ph S = Ph + 2B S L = ½Pl cube = 6s 2 V = Bh V rect prism = lwh V cube = s3 S = L + B S = ½Pl + B L = 2πrh S = L + 2πr2 S = 2πrh + 2πr2 V = Bh V = πr2h 4 Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Round to the nearest tenth, if necessary. 5 Find the lateral area and surface area of the pyramid. HINT:Use the Pythagorean Theorem to find ℓ. 6 Find the surface area of the composite figure. Surface Area of Cube without the top side: Surface Area of Pyramid without base: 7 HOMEWORK: # 82 Pyramid Worksheet L & S 8