Question

find the area of the given square. image of square with inscribed circle, radius 8 yd 100 yd² 70.86 yd² 256 yd² 3,556 yd²

Explanation:

Step1: Determine the side length of the square

The circle is inscribed in the square, so the diameter of the circle is equal to the side length of the square. The radius of the circle is \(8\) yd, so the diameter \(d = 2r = 2\times8 = 16\) yd. Thus, the side length \(s\) of the square is \(16\) yd.

Step2: Calculate the area of the square

The formula for the area of a square is \(A = s^2\). Substituting \(s = 16\) yd, we get \(A = 16^2 = 256\) \(yd^2\).

Answer:

\(256\) \(yd^2\) (corresponding to the option: \(256\) \(yd^2\))