Find the colored area

The shaded area is composed of $2$ sectors of a circle and $6$ segments of a circle. By some calculations the central angle of each is $45^\circ$ . Therefore the area of the shaded region is

$2\left(\dfrac{45}{360}\right)(\pi)(8^2)+6\left[\dfrac{45}{360}(\pi)(8^2)-\dfrac{1}{2}(8^2)(\sin 45)\right]\approx$ $\boxed{65.29743}$

8^2 π - 8^2sin(45)/2 * 6 = 65.2974...

You find the whole area of the circle, and subtract the 6 triangles using the law of sine: A = absin(C) which a and b are the sides and C is an angle in between. In this question the sides of the triangle are the radius. Using a calculater and these methods, you will be able to find and round the answer easily, which is 65.297 to the 3 decimal places.