Answer
$9\pi - 18$
Work Step by Step
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:
$9\pi - 18$
