RE: Math mini-contest problem for Day 2 on D.Buzz for April 2021 😎
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My answer is that the total area of all squares if you continue to do so infinitely will be 8 SQ inches.
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1st square has each side of length 2. Let this be x.
So the midpoint means that the length of the inner square is sqrt((x/2)^2 + (x/2)^2) = sqrt(2(x/2)^2) = sqrt(2). This means the area of the 2nd square is 2.
If we repeat this pattern, then the area of the following square is 1/2 of the previous square (I did the math and saw that this is true).
Leaving the sum of all squares using this as 4 + 2 + 1 + 1/2 +... and this summation leaves an answer of 8.