Question

square vwxy circumscribes circle z. find the area of the shaded region. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Calculate the area of the square

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 16\), then \(A_{square}=16\times16 = 256\).

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^2\). Since the diameter of the circle \(d = 16\), then the radius \(r=\frac{d}{2}=8\). So \(A_{circle}=\pi\times8^2=\pi\times64\approx3.14\times64 = 200.96\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{square}-A_{circle}\). Substitute the values: \(A = 256 - 200.96=55.04\approx55.0\).

Answer:

\(55.0\)