Math 310 Section 11.4 Surface Area

For a polygon, the surface area is the sum of all the areas of all the faces of the polygon. In this way it is similar to what you have already done for area, because each face will be a recognizable polygon that you already know how to find the area of. It will be different in that you have to sum several areas together, and remember that not every face is the same. We will also develop some formulas for common 3d figures.

Surface Areas of Common Figures We will find the surface area of the following figures: Right Prism Right Prism Cylinder Cylinder Pyramid Pyramid Cone Cone Sphere Sphere

Right Prism SA = (bases) + (lateral SA) Lateral SA = (perimeter of base)(height of figure)

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Cylinder SA = (bases) + (lateral SA) Lateral SA = ( circumference of base )( height of figure )

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Pyramid SA = (base) + (lateral SA) Lateral SA = sum of lateral faces

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Cone SA = (base) + (lateral SA) Base = πr 2 (remember, it’s a circle) Lateral SA = πrlwhere l = slant height

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Sphere SA = 4πr 2

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Now we put them together… When finding the surface area of a figure that isn’t one of the above, looking for combinations of the figures. Or sometimes the figures are deleted from each other. Just remember, break the problem into smaller pieces.

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