A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?
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A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?
Let the length of the sides of the original square be
, then the diameter of the circle cut-off from the square is 
.
Now, the diagonal of the square cut-off from the circle is equivalent to the diameter of the circle, thus
.
Now, the area of a square given the length of the diagonal is given by half the square of the length of the diagonal.
Therefore, the area of the square cut-off is
. That is half the square of the length of the sides of the original square.