## Groups of Ring Fields

Creator Challenge Difficulty Rating: **Medium**

### Problem

A farmer, known for his unusual aesthetics, planted five circular fields. Four of the circles have a one furlong radius and were arranged so their centers form a square and they are each tangent to two of the other three circles. The fifth field was planted in the area enclosed by the four circles such that it is tangent to all of them.

**What is the total area of the unplanted land enclosed by the five circles?**

In this image, the fields are shown in green. We are interested in measuring the red regions.