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%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Pyramid">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Wed Feb 12 19:10:21 1997}
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\section{\textbf{Pyramid \label{Pyramid}}}

Let $a=$ side of the (square) base, $h=$ height, and $s=$ slant height.

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\begin{itemize}
\item  The \label{Surface area of regular pyramid}\textbf{surface area} of a
regular pyramid is one-half the perimeter of the base times the slant height
plus the area of the base.

$S=a^{2}+2as=a^{2}+a\sqrt{2a^{2}+4h^{2}}$

\item  The \label{Volume of pyramid}\textbf{volume} of a pyramid is
one-third the height times the area of the base.

$V=\frac{1}{3}ha^{2}$
\end{itemize}

\begin{example}
If a regular pyramid has base of side $a=5$ and height $h=8$, then the
pyramid has surface area and volume 
\begin{eqnarray*}
S &=&5^{2}+5\sqrt{2\times 5^{2}+4\times 8^{2}}=25+15\sqrt{34}\approx
112.\,\allowbreak 46 \\
V &=&\frac{1}{3}\times 8\times 5^{2}=\frac{200}{3}
\end{eqnarray*}
\end{example}

\begin{example}
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\end{example}

the height is $h=\dfrac{a}{\sqrt{2}}\approx \allowbreak .\,\allowbreak
707\,11a$, the surface area is $S=3a^{2}$ and the volume is $V=\frac{1}{3}%
ha^{2}=\allowbreak \dfrac{\sqrt{2}a^{3}}{6}$.

\subsection{\ Related Reference Topics}

{\small \hyperref{Table of Geometric Formulas For Length, Area, and Volume}{%
}{}{TAB_geom_formulas.tex}}

{\small \hyperref{Trigonometry}{}{}{TR_contents.tex}}

\subsection{\ Related Scientific Notebook Topics}

{\small \hyperref{Angular Measure}{}{}{../../Help/DMIndex.tex#Angular measure%
}}

{\small \hyperref{Conic Sections}{}{}{../../Help/DMIndex.tex#Conic sections}}

{\small \hyperref{Plotting Curves and Surfaces}{}{}{../../Help/DM6.tex}}

{\small \hyperref{Polygons}{}{}{../../Help/DMIndex.tex#Polygons}}

{\small \hyperref{Surfaces of Revolution}{}{}{%
../../Help/DMIndex.tex#Surfaces of revolution}}

{\small \hyperref{Trigonometry}{}{}{../../Help/DM4.tex}}\hfill

\noindent \hrulefill

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