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Published byIsaiah Radner Modified over 2 years ago

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12.2 Surface Area of Prisms & Cylinders

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Definitions Prism – polyhedron with 2 faces (called bases) that lie in planes. –Named by the shape of the bases. Lateral Faces – the faces that are NOT bases (all are ’ogram shaped) Lateral Edges – edges of the lateral faces that are NOT edges of the bases as well. Height (altitude) - distance between the bases. Right Prism – lateral edges are to bases. Oblique Prism – lateral edges are NOT to the bases. (looks slanted)

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Right Oblique Triangular Prisms Bases (2 Δs) Lateral edges (3) Lateral faces (3 ll’ograms) height

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3-D Areas Lateral Area (LA) – the sum of the areas of the lateral faces only. –Does not include the area of the bases. Surface Area (S) – the sum of the areas of ALL the faces. –Lateral area + area of the bases

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Net Defn. – a 2-dimensional representation of a solid. Just think “unfold” the figure and lay it flat. Ex:

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To find surface or lateral areas, you could find the areas of each individual face and then add them all together; OR you could use formulas! Thm 12.2 – SA of a rt. Prism S = 2B + Ph B = area of base, P = perimeter of base, h = height of prism What about Lateral Area? * remember: LA is everything BUT the bases! So, LA = Ph

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Ex: Find the lateral & surface areas of the triangular prism. LA = Ph P = 6*3 = 18 LA = 18*10 LA = 180 in 2 S = 2B + Ph S = 2(15.59) S = S = in 2 6 in. 10 in. 60 o

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Cylinder Defn. – solid with , circular bases. Can be oblique or right. Lateral Area – the area of the curved surface. What does the curved surface look like if laid out flat? Think of the label of a soup can! It’s a rectangle! (area of rectangle = bh) Surface Area – lateral area + area of bases. h h

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Thm 12.3: SA of a rt. cylinder Let’s look at lateral area 1 st ! LA = Ch or LA = 2 rh So, S = 2B + Ch or S = 2 r rh

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Ex: Find the lateral & surface areas of the cylinder. LA = 2 rh LA = 2 (4)(8) LA = 64 m 2 Or m 2 S = 2 r rh S = 2 (4 2 ) + 64 S = 32 + 64 S = 96 m 2 Or m 2 8 m. 4 m.

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