What is the area of this square

I am really confused. On my geometry homework there is a problem that says a square has the radius of 8 inches. I used this to find that the sides are also 8 inches and found that A=8*8 which is 64in^2. To check my work I treated the square like a rhombus and used the formula A=1/2*d1*d2, but by doing this I got 128in^2. I then did one final formula and treated it as a regular polygon, but by doing this I got the answer A=110.85in^2 (after rounding). What am I doing wrong and which of my answers is correct?

Radius" is a term most commonly associated with circles. When used in reference to a square, the radius is the distance from the center of the square to any of the four vertices. A vertex is where two sides intersect. Because a square has four right angles, you can find the diameter of the square using the Pythagorean Theorem.

Lent the length of the radius be r and the length of a side be s.
Now make a little sketch and you will see that r^2 = (s/2)^2 + (s/2)^2 (per Pythagoras)

r^2 = 2(s/2)^2 = s^2/2, so s^2 = 2r^2

but s^2 is the area of the square......, so your answer should be 2 x 8^2 = 128

OK?

First of all, the correct statement of the question should found out.
The correct statement may be :
1) a circle inscribed in a square has the radius of 8 in. Or,
2) a circum circle of a square has the radius of 8 in.

The radius I a aware in sonnet the length of a side, but the distance from the center to one I the corners. Then, you use the Pythagorean theorem to find each side is actually 4 in long. So the area is 16 in^2.

I agree. it is confusing. Squares do not have a radius. They have sides & diagonals. The diagonal is the square root of 2 ( = 1.4142135) times the side.