Well, before we get into actual figures, you can tell right away just by looking
at this thing that something's wrong. Pretty much everybody knows that inches
are smaller than feet, which leads us to suspect right away that a smaller number
of square inches probably can't be equal to a bigger number of square feet.
In this case, I think I know what went wrong, and it falls in the non-mathematical
category of proof-reading. The numbers are correct, but the labels are swapped.
The question was either inadequately proof-read, or else it was carelessly copied
out of the book.
186,624 square inches is the same amount of area as 1,296 square feet
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18inx18in = 324 sqin = 2.25sqft (1 sqft = 144 sqin) 200 / 2.25 = 88.89 tiles
16' 2" = 194" and 23' 11" = 287" so we multiply these inches together194 * 287 = 55678 square inches (386 sqft and 94 sqin)
5.5 x 5.5 x pi sqin = just over 95 sqin
6 sqin
225 sqin