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Surface Area of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder.

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I. Surface Area of a Prism Prism – Is a polyhedron with exactly 2 , // faces, called bases. Name it by the shape of its bases. Bases are Rectangles: Lateral Faces – All faces that are not bases. (Sides)

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Right Prisms vs Oblique Prisms Right Prism – Edges are Altitudes. Oblique Prism

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Lateral Area – The sum of the areas of the lateral faces (sides) Right Prisms - Lateral Faces are Rectangles A = lw Base Area – The sum of the areas of the 2 bases Rectangle: A = lw Triangle: A = ½bh Polygon: A = ½bh Total Surface Area = Lateral Area + Base Area

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Ex.1: Use the net to find the Surface Area of the rectangular Prism. 5cm 3cm 4cm Area of Bases: A = lw 12 2 different Lats: A = lw SA = LA + Area of Bases = 70cm cm 2 = 94cm 2

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Ex.2: Find the total surface area of the following triangular prism. 6cm 5cm 12cm LA = lw (Area of Sides) (5 x 12) = 60cm 2 (6 x 12) = 72cm 2 BA = ½bh = ½(6)(4) = 12cm 2 x 2 x 2 24cm 2 a 2 + b 2 = c 2 h = 5 2 h = h 6 192cm 2 SA = LA + BA = 192cm cm 2 = 216cm 2 Area of Triangle

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Ex.2: Find the total surface area of the following regular hexagonal prism. LA = lw (10 x 12) = 120m 2 x 6 BA = ½ap = ½(8.7)(60) = 260m 2 x 2 520m 2 720m 2 SA = LA + BA = 720m m 2 = 1240m 2 10m 12m ° a Tan 30 = 5/a.577 = 5/a a = 8.7

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II. Finding Surface Area of a Cylinder Cylinder Has 2 , // bases Base → Circle C = 2πr A = πr 2 height r r h r

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Net of a Cylinder: LA is just a Rectangle! LA = 2 rh r BA = r 2 Area of a circle Circumference of the circle SA = LA + 2BA

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Ex.4: SA of a right cylinder 6ft 9ft LA = 2 rh = 2 (6)(9) = 108 ft 2 = 339.3ft 2 Area of Base BA = r 2 = (6) 2 = 36 ft 2 x 2 = 72 ft 2 = ft 2 SA = LA + BA = 339.3ft ft 2 = 565.5ft 2

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What did I learn today?? Find the area of the lateral sides first!! Usually rectangles Be careful, the rectangles are not always the same size. Second, find the area of the Base Rectangle, Triangle, Polygon, or a Circle There are always 2 bases in prisms. Multiply by 2!

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