\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}

\begin{document}
\begin{preview}
\begin{tikzpicture}
    % Draw axes
    \draw [<->,thick] (0,2.5) node (yaxis) [above] {$x_2$}
        |- (2.5,0) node (xaxis) [right] {$x_1$};

    % Draw two intersecting lines
    \draw[thick, dashed] (1,1) coordinate (a) -- (2,1) coordinate (b);
    \draw[thick, dashed] (a) -- (1,2) coordinate (d);
    \draw[thick]         (d) -- (2,2) coordinate (c);
    \draw[thick]         (b) -- (2,2);

    \fill[green!15] (a) -- (b) -- (c) -- (d) -- (a);

    % Draw lines indicating intersection with y and x axis. Here we 
    % use the perpendicular coordinate system
    \draw[dotted] (yaxis |- a) node[left] {$a_2$}
        -| (xaxis -| a) node[below] {$a_1$};

    \draw[dotted] (yaxis |- c) node[left] {$b_2$}
        -| (xaxis -| c) node[below] {$b_1$};
\end{tikzpicture}
\end{preview}
\end{document}