Question

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

answer
attempt 1 out of 2

Explanation:

Step1: Find area of the square

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

Step2: Find area of the circle

The square circumscribes the circle, so the diameter of the circle is equal to the side length of the square, which is 16. Thus, the radius \( r = \frac{16}{2} = 8 \). The formula for the area of a circle is \( A_{circle} = \pi r^2 \).
\( A_{circle} = \pi (8)^2 = 64\pi \)

Step3: Find area of the shaded region

The shaded region is the area of the square minus the area of the circle.
\( A_{shaded} = A_{square} - A_{circle} = 256 - 64\pi \)

Calculating the numerical value: \( 64\pi \approx 64\times3.1416 \approx 201.06 \)
\( A_{shaded} \approx 256 - 201.06 = 54.94 \approx 54.9 \) (rounded to the nearest tenth)

Answer:

\( 256 - 64\pi \) (or approximately \( 54.9 \))