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In the figure below, a circle with radius r is inscribed within a square. What is the area of the shaded region?

A $4480_w70_h20.png$

Since the square is circumscribed, its side is twice the length of the radius, or 2r, and its area is $2934_w24_h17.png$. The area of the circle is given by $7872_w26_h16.png$. The shaded area is the difference between these two, or $4480_w70_h20.png$