In a currently-recent (but by the time you read this, long in the past) Chalkdust ((It’s a magazine for the mathematically curious)), @cshearer42 gave a puzzle that caught my eye.

One of the things I love about Catriona’s puzzles is that you usually get two-for-the-price-of-one: there’s “getting the right answer”, which is not usually hard, and there’s “getting the answer elegantly”, which is rewarding.

Below the line are spoilers.

Tackling it tired, I took a bit of a sledgehammer to it: the line resting on the top-left of the lower-right 16-square has a gradient of $\frac{1}{2}$, so it cuts the outer square midway up the right edge.

Similarly ((ha!)), the other line from the bottom-left corner has a gradient of two and cuts the upper edge at its midpoint.

A symmetry argument means the target square’s lower edge is then three-quarters of the way up the main square; the big square’s edge length is 12, so the target square has side length of 3 and area 9.

Ugh.