Acircle with circumference 12 has an arc with a 330° central angle.

1

Step-by-step explanation:

There are a few ways to solve this problem.

Here is one method:

I am going to use the arc formula and change 330 degrees to radian

Our angle = 360 - 330 = 30 degrees

Transform angle from degrees to radian

30 degrees =

Now that we have our angle, we need the radius. (r)

Ok, we have all of our parts so it is time to find the length of the arc by using our arc formula

s = 1

The arc length = 1

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2