Fractions of a square

I liked this tweet:

I have a solution for the Q below but it is very algebraic & not particularly elegant: anyone see a more visual way? pic.twitter.com/iuf07jPN83

— Michael Jacobs (@msbjacobs) September 14, 2015

and saw there was at least one ingenious way to solve it:

@msbjacobs This one uses the Carpets Theorem but I'm sure it can be proof in many other ways. pic.twitter.com/25lXGJdiSp

— Carlos Luna (@el_luna) September 15, 2015

I looked at it like this:

and it reminded me of this:

(The yellow square is one fifth of the big square. There's a proof here.)

So, I could see here that the diagonal was divided into thirds. After a bit of thrashing around, I could also see that the green triangle must be ⅙ of the whole square.

@msbjacobs @el_luna ... then, because ▲s with the same base and height have = area, the yellow and the green are =. pic.twitter.com/iO6XQBmJjr

— Simon Gregg (@Simon_Gregg) December 3, 2015

I like the way the square is divided so simply up into fractions. There are halves and quarters:

and all sorts of other possibilities:

Oh - that would make a good Which One Doesn't Belong?

It strikes me that it would make a good shape for students to divide up in different ways like this.

In the same way that they have here:

Great quarter activity, @GraemeAnshaw @mburnsmath https://t.co/0T4GzF46WT pic.twitter.com/uCygYuxM9K

— Simon Gregg (@Simon_Gregg) November 5, 2015

And then there's the one fifth square...