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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.

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**Lateral Area – The sum of the areas of the lateral faces (sides)**

Right Prisms - Lateral Faces are Rectangles A = l•w Base Area – The sum of the areas of the 2 bases Rectangle: A = l•w 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.**

Area of Bases: A = l•w 2 different Lats: A = l•w 4 5cm 12 3 3 4 3 5 15 20 15 20 3cm 4cm SA = LA + Area of Bases = 70cm2 + 24cm2 = 94cm2 3 12

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**Ex.2: Find the total surface area of the following triangular prism.**

5cm LA = l•w (Area of Sides) (5 x 12) = 60cm2 (6 x 12) = 72cm2 5cm 12cm 6cm Area of Triangle 192cm2 BA = ½bh = ½(6)(4) = 12cm2 x 2 24cm2 5 3 h SA = LA + BA = 192cm2 + 24cm2 = 216cm2 a2 + b2 = c2 h = 52 h = 4 6

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**Ex.2: Find the total surface area of the following regular hexagonal prism.**

LA = l•w (10 x 12) = 120m2 x 6 12m 720m2 10 BA = ½ap = ½(8.7)(60) = 260m2 x 2 520m2 10m 30° a SA = LA + BA = 720m m2 = 1240m2 5 Tan 30 = 5/a .577 = 5/a a = 8.7

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**II. Finding Surface Area of a Cylinder**

Has 2 , // bases Base → Circle C = 2πr A = πr2 r height r h r

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**Net of a Cylinder: LA is just a Rectangle! LA = 2rh BA = r2**

Area of a circle LA = 2rh BA = r2 r Circumference of the circle SA = LA + 2BA

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**Ex.4: SA of a right cylinder**

LA = 2rh = 2(6)(9) = 108ft2 = 339.3ft2 6ft Area of Base BA = r2 = (6)2 = 36ft2 9ft x 2 SA = LA + BA = 339.3ft ft2 = 565.5ft2 = 72ft2 = ft2

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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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