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.