Puzzle: how would you divide the land equally? (spoilers)

While I normally post math puzzles on Monday, I found another interesting puzzle so there is a bonus problem this week.

Here is the problem.

A father dies and wants to divide his land evenly amongst four sons. The plot of land has the following unusual shape:

How can you divide the land into four equal parts, using only straight lines?

Give it a try before reading the answer below.

SPOILER ALERT: don’t scroll until you are ready. Solution is just below

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I came across this puzzle when it was presented to gifted math students.

Several of the high school students them were able to come up with the following solution.

I feel like this is the type of solution one might come up with–it is symmetric and somehow “makes sense.”

One of the students had shown a lot of creativity in his work. He came up with the above solution, but he also submitted a second answer that definitely took me by surprise, as follows.

It is amazing to see how the shape can be divided into four parts using scaled down versions of itself. Well done if you came up with this answer on your own.

(I would love to see what would happen if you iterate the process: take each of the four small pieces and divide them again into four small pieces. I could not figure out a quick way to do this working manually–if someone figures it out I’d love to see the shape if there is an interesting fractal pattern to it.)

[Edit 9-16]: V Paul Smith has taken up the challenge and done a manual tessellation. Here is what it looks like. It’s absolutely beautiful (click on it to see the full image)