Midpoint? What About Thirds? - Part 2

Geometry Level 4

Just like in Part 1, \(ABCD\) is a square with a side length of 18, and we 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 \(D\). This time, we connect each of those points to the nearest vertex that is opposite to them to form a not-necessarily-regular octagon as shown in the figure above, for example, points \(A\) and \(E\) will be connected in this case. What is the area of this octagon?


You may wish to try Part 1 and Part 3 of this trilogy.
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