Question

square hijk circumscribes circle l. 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 \(s = 10\), then \(A_{square}=10\times10 = 100\).

Step2: Calculate the area of the circle

The diameter of the circle \(d\) is equal to the side - length of the square, so \(d = 10\), and the radius \(r=\frac{d}{2}=5\). The formula for the area of a circle is \(A=\pi r^2\). Substituting \(r = 5\) into the formula, we get \(A_{circle}=\pi\times5^2=25\pi\approx25\times3.14 = 78.5\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A_{shaded}=A_{square}-A_{circle}\). Substitute the values of \(A_{square}\) and \(A_{circle}\) into the formula: \(A_{shaded}=100 - 78.5=21.5\).

Answer:

\(21.5\)