Question 30
Consider pentagon ABCDE with $\angle BAE=\angle CBA=90^\circ$, $AE=BC$ and $ED=DC$. Four points divide AB into five equal parts. Vertical lines through them divide the figure as shown. The dark middle part has area $13\,\mathrm{cm}^2$ and the lightly shaded part just left of it has area $10\,\mathrm{cm}^2$. What is the area of the whole pentagon in $\mathrm{cm}^2$?
