Midpoint? What About Thirds? - Part 3

Geometry Level 4

As usual, ABCDABCD is a square, and we divide each side​ into three equal parts, and mark the points E,F,G,H,I,J,K,LE,F,G,H,I,J,K,L in a clockwise manner starting from the vertex DD. This time, we connect those points to the furthest vertex that is opposite to them to form a not-necessarily-regular octagon as shown in the figure above, for example, points BB and EE will be connected in this case. What is the ratio of the area of the square to that of the octagon?


You may wish to try Part 1 and Part 2 of this trilogy.
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