Problem of the Month March 2015 Mar 15, 2015

A goat is tethered to a (circular) silo of radius r. The length of the rope is just long enough so that the the goat can make if halfway around the silo (at which point it will be right against the silo's wall). No other objects are nearby. Determine the area of the region where the goat can graze.

This is a classic problem. See if you can figure out without looking it up!