The length of each side of the second regular octagon is exactly half the length of each side of the first ocagon, i.e. 10.9 / 2 = 5.45. So, the area of the second octagon is exactly 1/2 * 1/2 = 1/4 the area of the first octagon, which is 392.4 / 4 = 98.1 in².
So the answer is = 98.09 in2