Xmas Puzzle 2019(2)

I discussed this one over breakfast with my daughter, our answer in PM. We hope to hear if we got it right. Thanks for the puzzle, we quite enjoyed our breakfast.
 
Different approach than mine, I did get the same answer. I started assuming a unit circle (radius 1), which eventually gave me sides of the square equal to 8/5. Then scaled up with the h=1 value, which was 2/5 for a unit circle. Side of the squares then becomes (8/5)/(2/5) = 8/2 = 4, leading to a surface of 4x4=16.
 

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