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\begin{document}

%-------------------------------------------------------------------

\section*{dissected hexagon solution}

\hypertarget{dissected_hexagon}{}\section*{{Dissected Hexagon}}\label{dissected_hexagon}

[[DissectedHexagon.png:pic]]

\begin{quote}%
What fraction of this regular hexagon is not covered by the two isosceles triangles?


\end{quote}
\hypertarget{solution_by_properties_of_a_regular_hexagon_and_area_of_a_triangle}{}\subsection*{{Solution by [[Properties of a Regular Hexagon]] and [[Area of a Triangle]]}}\label{solution_by_properties_of_a_regular_hexagon_and_area_of_a_triangle}

[[DissectedHexagonLabelled.png:pic]]

Drawing the line segment $E D$ in the above diagram shows that the unshaded region comprises six [[congruent]] triangles. Each has base one half of the side length of the hexagon and height one half of its height. The [[regular hexagon]] itself comprises six [[congruent]] [[equilateral triangles]], each with base one side length of the hexagon and height one half of its height. Therefore, each of the thinner triangles has area half of that of one of the equilateral triangles, and so the unshaded area comprises half the hexagon.



\end{document}