Answer:
s^2
Explanation:
Let s be the length of the side of the original square piece. The maximum circle that can be inscribed in the square has a diameter of s, or a radius of s/2. Now, to inscribe a square in this circle, its maximum dimension, the diagonal, will be equal to the diameter of the circle, s. This square will have sides of s/SQRT(2), and so have an area of s^2/2. Since the area of the original piece is s^2, exactly one half of the area has been chopped off in this rather wasteful metal shop procedure.