Question 34543
1) A square whose area is 16 has sides of 4.
2) If partitioned into four congruent squares, the smaller squares will have sides of 2.
3) The center of the smaller squares will be at a distance of{{{sqrt(2)}}} from the center of the parent square.
4) The radius of the circle whose circumference contains the centers of the four smaller squares will be{{{sqrt(2)}}}.
5) The area of the circle is:
{{{A = (pi)r^2}}}
{{{A = (pi)(sqrt(2))^2}}}
{{{A = 2(pi)}}} 

If statement 3) is not obvious, here's how I determined that.

From the center of one of the smaller squares, drop a perpendicular to one of its sides thus bisecting that side. You will have formed a right triangle whose legs are 1 each and whose hypotenuse is{{{sqrt(2)}}} (See Pythagorean theorem).
The hypotenuse is the radius of the circle.