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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 faces (3 ll’ograms) height Lateral edges (3) Triangular Prisms

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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 lie 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 SA = 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.**

6 in. 60o 10 in.

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**Cylinder Defn. – solid with , circular bases.**

Can be right or oblique. Lateral Area – the area of the curved surface. What does the curved surface look like if lied 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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**Let’s look at lateral area 1st! So, SA = 2B + Circumference × h**

Thm 12.3: SA of a rt. cylinder Let’s look at lateral area 1st! LA = Circumference × h or LA = 2rh So, SA = 2B + Circumference × h SA = 2r2 + 2rh

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**Ex: Find the lateral & surface areas of the cylinder.**

LA = 2rh LA = 2(4)(8) LA = 64 m2 SA = 2r2 + 2rh SA = 2(42) + 64 SA = 32 + 64 SA = 96 m2 4 m. 8 m.

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Bell Ringer Find the surface area of each figure. SA = 2lw + 2lh + 2wh SA = 2(4*2) + 2(4*3) + 2(2*3) SA = 16 + 24 + 12 SA = 52 units² SA = Area of Base.

Bell Ringer Find the surface area of each figure. SA = 2lw + 2lh + 2wh SA = 2(4*2) + 2(4*3) + 2(2*3) SA = 16 + 24 + 12 SA = 52 units² SA = Area of Base.

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