The value of 122 is between which two integers

I am assuming you mean the square root of 122

11^2 < 122 < 12^2

121< 122< 144

so 11 < sqrt(122) < 12

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

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.