Question

square ijkl circumscribes circle m. 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 diameter of the circle is equal to the side length of the square. Given the radius \(r = 6.5\), the diameter \(d=2r = 13\).
The area of the square \(A_{square}=s^{2}\), where \(s = 13\). So \(A_{square}=13^{2}=169\).

Step2: Calculate the area of the circle

The area of a circle is \(A_{circle}=\pi r^{2}\), with \(r = 6.5\). So \(A_{circle}=\pi\times(6.5)^{2}=\pi\times42.25\approx 132.7\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{square}-A_{circle}\).
\(A=169 - 132.7=36.3\).

Answer:

\(36.3\)