Each exterior angle of a regular hexagon is 60° (360° /
6), so when sides HB and
IC are extended to meet
at A , an equilateral
triangle, ABC is
created. Let the sides of this triangle be of length x. As BC, DE and FG are all parallel, triangles
ABC, ADE and
AFG are all equilateral.
So, < span style="font-style: italic;»DE < /span > = < span style = "font-style: italic;»DA < /span > = p + x; and < span style = "font-style: italic;»FG < /span > = < span style = "font-style: italic;»FA < /span > = q+p+x.