Midpoint? What About Thirds?

Geometry Level 4

ABCDABCD is a square with a side length of 18. 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. Then, connect the points to get a not-necessarily-regular octagon as shown in the figure above. What is the area of the octagon?

Bonus: You may notice that the ratio between the segments of all the sides are all 1:1:11:1:1. Now, generalize this by considering the case of 1:k:11:k:1, where kNk\in\mathbb{N}.


You may wish to try Part 2 and Part 3 of this trilogy.
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