The figure below shows an equilateral
triangle ABC of area S. P is any point and PD, PE, and PF are perpendicular to AB, BC,
and AC, respectively. If S_{1}, S_{2}, S_{3}, S_{4}, S_{5}, and S_{6} are the areas of the shaded regions,
prove that S_{1}+S_{3}+S_{5} = S_{2}+S_{4}+S_{6} = S/2. This entry contributed by Ajit Athle.
