Question

square vwxy circumscribes circle z. find the area of the shaded region. round your answer to the nearest tenth if necessary. image of square with circle inside, radius of circle is 9

Explanation:

Step1: Find the side length of the square

The radius of the circle is 9, so the diameter (which is equal to the side length of the square) is \( 2\times9 = 18 \).

Step2: Calculate the area of the square

The area of a square is \( \text{side}^2 \), so the area of square \( VWXY \) is \( 18^2 = 324 \).

Step3: Calculate the area of the circle

The area of a circle is \( \pi r^2 \), with \( r = 9 \), so the area is \( \pi\times9^2 = 81\pi \approx 81\times3.1416 = 254.4696 \).

Step4: Find the area of the shaded region

The shaded region area is the square's area minus the circle's area: \( 324 - 254.4696 = 69.5304 \). Rounding to the nearest tenth gives approximately 69.5.

Answer:

\( 69.5 \)