%\bigskip
%\noindent\textbf{\large Triangle Areas}
\section{Triangle Areas}

%%\begin{displaymath}
%%  A = \frac{1}{2} b h
%%\end{displaymath}

If vertices of triangle, $(x_i, y_i)$ are known,
\begin{displaymath}
  A = \frac{1}{2}
       \left|
         \begin{array}{ccc}
           x_1 & x_2 & x_3 \\
           y_1 & y_2 & y_3 \\
           1 &   1   & 1 
         \end{array}
       \right|
\end{displaymath}
This is a \textsl{signed} area.  Counterclockwise around
the triangle will give a positive area.  Clockwise gives
a negative area.

If the lengths of the sides are known, 
\begin{displaymath}
  A = \sqrt{s (s - a)(s - b)(s - c)}\ \ \ 
  s = \frac{1}{2}(a + b + c)
\end{displaymath}

See also Intersection.java at the back of the packet.

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