## Elementary Geometry for College Students (6th Edition)

$9\pi - 18$
We know that the triangle only coincides in half of the circle. Thus, the area of the circle around the triangle is: $A = \pi(6^2) \times 1/2 = 18\pi$ We know that, since the triangle forms a 45-45-90 triangle when cut in two, each side is $6\sqrt2$. This means that the area is: $A = 1/2(6\sqrt2)(6\sqrt2) = 36$ Thus, the area of both regions is: $A = 18\pi-36$ This means that the area of one region is: $9\pi - 18$