Puzzle of the Week #140 - Rational Area

The diagram shows 6 identical circles, arranged such that the centre of each lies on the circumference of others, in a right angled grid pattern. This results in 23 regions (A to W). Assuming that the radius of the circles is a rational number, the area of each of the regions will be an irrational number, being dependent not just on the radius, but also on pi.

6 circles.JPG

How can you combine a number of contiguous regions to form a combined area that is rational?