\begin{frame}
  \frametitle{Motivation and Overview}

  How to compute the area of a polygon?
  \begin{center}
  \begin{tikzpicture}[default,scale=.5]
    \begin{scope}[inner sep=0,outer sep=0]
    \draw (0,0) -- node[at start] (1) {} 
          ++(-3,-1) -- node[at start] (2) {} 
          ++(-1,-2) -- node[at start] (3) {}
          ++ (1,-2) -- node[at start] (4) {}
          ++(3,-1) -- node[at start] (5) {} node[at end] (6) {}
          ++ (2,3) -- 
          cycle;
    \end{scope}
    \begin{scope}[cred,dashed]
    \mpause[2]{ 
    \draw (6) -- node[pos=.7] (m1) {} node[pos=.5] (m1') {} (2);
    \draw (6) -- node[pos=.7] (m2) {} (3);
    \draw (6) -- node[pos=.7] (m3) {} node[pos=.5] (m3') {} (4);
    }
    \mpause[3]{ 
    \node at ($(1)!.5!(m1')$) {$A_1$};
    \node at ($(m1)!.5!(m2)$) {$A_2$};
    \node at ($(m2)!.5!(m3)$) {$A_3$};
    \node at ($(m3')!.5!(5)$) {$A_4$};
    }
    \end{scope}
  \end{tikzpicture}    
  \end{center}
  \pause
  The ancient Greek did it as follows:
  \begin{itemize}
  \pause
    \item divide the polygon into triangles
  \pause
    \item compute the area of the triangles (and sum them up)
  \end{itemize}
\end{frame}