# Surface Area of Prisms & Cylinders

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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.

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)

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

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

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

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

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

II. Finding Surface Area of a Cylinder
Has 2 , // bases Base → Circle C = 2πr A = πr2 r height r h r

Net of a Cylinder: LA is just a Rectangle! LA = 2rh BA = r2
Area of a circle LA = 2rh BA = r2 r Circumference of the circle SA = LA + 2BA

Ex.4: SA of a right cylinder
LA = 2rh = 2(6)(9) = 108ft2 = 339.3ft2 6ft Area of Base BA = r2 = (6)2 = 36ft2 9ft x 2 SA = LA + BA = 339.3ft ft2 = 565.5ft2 = 72ft2 = ft2

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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