Christopher Danielson’s square problem

Saw an interesting problem on twitter last night:

with this one extra clarification on the shape:

Seems like a good problem for a kid learning geometry, so I tried it out with my older son tonight. First we looked at the two twitter posts to make sure that he understood the problem and I asked him to come up with a plan for how to solve it:

 

Next we went to the white board to work out the solution. He did a good job following through on this plan, which was nice. One thing that I thought might give him a little difficult was that the 4th root of 3 appears in his solution. However, he did not simplify the numbers in the problem the way I expected him to, so the 4th root of 3 didn’t appear 🙂

 

Definitely a fun little problem. One alternate problem that I skipped because I thought it would be too difficult was finding the area of a different square hiding in Danielson’s picture. The “center” of the 4 pointed star is also a square – what area does it have if the kites have area 1?

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