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Derive Formulas of Surface Area – Right Prisms and Right Cylinders

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Definition of a Prism A Prism is a solid having bases or ends that are parallel, congruent polygons and sides that are parallelograms. http://dictionary.reference.com/browse/prism

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Parts of a Right Prism The bases are congruent and parallel The lateral faces are the faces connecting the corresponding vertices of the bases Lateral edges are the segments connecting the lateral faces

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Different Right Prisms All Prisms with a Right angle

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Oblique Prism A prism that has lateral edges that are not perpendicular to the bases.

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Height vs. Slant Height

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A way to show the surface of a Prism A two Dimensional representation of a prism is called a net

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Another way is adding all the faces and bases The equation S.A. = 2(W·H + W·L + H·L) W = 4; L = 7; H = 5

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To find surface area of a rectangular prism S.A. = 2(2 x 4) + 2(3 x 4) + 2(2 x 3) S.A. = 2(8) + 2(12) + 2(6) S.A. = 16+ 24+ 12 S.A. = 52

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Let’s Derive Surface Area Prism SA = 2lw + 2wh + 2lh SA = 2lw + h(2w + 2l) SA = 2 bases + h ⋅ perimeter

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Surface Area of a Right Prism Theorem 12.2 The Surface Area of a Prism is the sum of two base areas and the lateral face areas. Lateral faces = Height times Perimeter B is area of a base P is perimeter of the base H is height

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Right Prism Theorem The Base is 4(7)= 28 Perimeter is 2(4)+2(7) = 22 Height is 5 S.A. = 2(28) + 22(5) S.A. = 166

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Your Turn!!! Find the surface area The bases are 12x2 S.A. = 2B+Ph S.A. = 2(12x2) + 28x7 S.A. = 48+196 S.A. =244 cm 2 Perimeter = 24 + 4 H= 7 The bases are (11x17)/2 Perimeter = 11 +17 +20 H = 6 S.A. = 2B+Ph S.A. = 2(11x17)/2+ 48x6 S.A. = 187+ 288 S.A. =475 cm 2

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Define of a Cylinder A Prism with a circular base

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The net of a Cylinder Two circles and a Rectangle

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The Surface Area of a Cylinder 2 Bases + Circumference times height

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The Surface Area of a Cylinder 2 Bases + Circumference times height

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