Four circles, each of radius 1, intersect as shown. What is the perimeter of the shaded region? So let's take a look at this intersection portion right here. So this circle and this circle have the same radius. So that means this length and this length have to be the same. And similarly for the other two intersections. The perimeter of the shaded region is this red portion, plus the yellow portion, plus the green portion, along with these three middle portions. So if we just use the other red, yellow, and green portions, now it's the perimeter of this circle. This circle has radius 1, and so the perimeter is 2 pi times the radius, which is 2 pi times 1, so our final answer is 2 pi.

circle

intersection

perimeter

radius

geometry