CK12 - Geometry

(Marvins-Underground-K-12) #1

SurfaceAreaof a RegularPyramid


To get a generalformulafor the area of a regularpyramid,look at the net for this squarepyramid.


The slantheightof eachlateraltriangleis labeled (the lowercaseletter ), and the side of the regular
polygonis labeled. For eachlateraltriangle,the area is:


Thereare trianglesin a regularpolygon—e.g., for a triangularpyramid, for a square


pyramid, for a pentagonalpyramid.So the total area, , of the lateraltrianglesis:


If we rearrangethe aboveequationwe get:


Noticethat is just the perimeter, , of the regularpolygon.So we can substitute into the equation
to get the followingpostulate.


To get the total area of the pyramid,add the area of the base, , to the equationabove.

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