# Derive Formulas of Surface Area – Right Prisms and Right Cylinders.

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Derive Formulas of Surface Area – Right Prisms and Right Cylinders

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

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

Different Right Prisms All Prisms with a Right angle

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

Height vs. Slant Height

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

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

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

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

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

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

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

Define of a Cylinder A Prism with a circular base

The net of a Cylinder Two circles and a Rectangle

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

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

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