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 \(k\in\mathbb{N}\).


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

Problem Loading...

Note Loading...

Set Loading...