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12-2 Surface Area of Prisms You found areas of polygons. Find lateral areas and surface areas of prisms. Find lateral areas and surface areas of cylinders.

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Definition A prism is a polyhedron with two identical polygonal faces called bases that lie in parallel planes. The other parallelogram-shaped faces are lateral faces. Where lateral faces intersect are lateral edges. The altitude is a perpendicular segment that joins the planes of the bases. The height is the length of the altitude

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Altitude or Height? An altitude of a prism is a segment perpendicular to both bases whose endpoints are in the planes of the bases. The length of an altitude is the height of the prism. Altitude

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Right or Oblique? Right prism—the lateral edges of the prism are perpendicular to its bases. Oblique prism---the lateral edges of the prism are not perpendicular to its bases. Classify each prism.

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Lateral Area b Sides only No bases

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Lateral area is the sum of the areas of the lateral faces of a prism. The lateral area of a right prism is the product of the perimeter of its base and the height of the prism. L = Ph p. 846

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Find the lateral area of the regular hexagonal prism. The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters. Answer:The lateral area is 360 square centimeters. Lateral area of a prism P = 30, h = 12 Multiply.

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Find the lateral area of the right prism with right triangular bases. Ask: What is the shape of the base? Triangle Find the triangle LA formula 6 8 10 9

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A.162 cm 2 B.216 cm 2 C.324 cm 2 D.432 cm 2 Find the lateral area of the regular octagonal prism.

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Surface Area The surface area of the prism is the total area of all of its faces including the bases. The surface area of a right prism is the sum of its lateral area and the areas of its bases. S = L + 2B or S = PH+2B p. 846

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Surface Area SA = P h + 2 B or

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Find the surface area of the rectangular prism. Answer:The surface area is 360 square centimeters. Surface area of a prism L = Ph Substitution Simplify.

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Find the surface area of the right prism with right triangular bases. Ask: What is the shape of the base? Triangle Find the triangle SA formula 6 8 10 9

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A.320 units 2 B.512 units 2 C.368 units 2 D.416 units 2 Find the surface area of the triangular prism.

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Lateral Area and Surface Area Look at the top of your formula chart. The first question you need to ask is: What shape is the base? Find the shape at the top. Then ask, what kind of figure is it and go to that formula. There is a key for all of the abbreviations at the bottom of the page.

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12-2 Assignment Page 850, 9-17 skip 10 NO FORMULAS WITH NUMBERS NO CREDIT

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