# Midpoint? What About Thirds?

Geometry Level 4

$$ABCD$$ is a square with a side length of 18. Divide each side​ into three equal parts, and mark the points $$E,F,G,H,I,J,K,L$$ in a clockwise manner starting from the vertex $$D$$. 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 $$1:1:1$$. Now, generalize this by considering the case of $$1:k:1$$, where $$k\in\mathbb{N}$$.

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