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\begin{document}

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

\section*{areas in a crossed trapezium solution}

\hypertarget{solution_to_the_areas_in_a_crossed_trapezium_puzzle}{}\section*{{Solution to the Areas in a Crossed Trapezium Puzzle}}\label{solution_to_the_areas_in_a_crossed_trapezium_puzzle}

[[AreasinaCrossedTrapezium.png:pic]]

\begin{quote}%
The total blue area is equal to the purple area. What fraction of the trapezium is shaded?


\end{quote}
\hypertarget{solution_by_crossed_trapezium}{}\subsection*{{Solution by [[Crossed Trapezium]]}}\label{solution_by_crossed_trapezium}

As shown on the page on [[crossed trapezium]], the two blue triangles have the same area and the area scale factor from the white triangle to each of the blues is the same as from each of the blues to the purple. Since the purple triangle has twice the area of each blue, each blue therefore has twice the area of the white and the purple has four times the area of the white. The full trapezium is nine ($4 + 2 + 2 + 1$) times the size of the white triangle, so $\frac{8}{9}$ths of it is shaded.



\end{document}