Question

find the area of the yellow shaded region. round to the nearest tenth

Explanation:

Step1: Calculate the area of the square

The area formula for a square is \(A = s^2\), where \(s = 6\) in.
\(A_{square}=6\times6 = 36\mathrm{in}^2\)

Step2: Calculate the area of the circle

The diameter of the circle \(d = 6\) in, so the radius \(r=\frac{d}{2}=3\) in. The area formula for a circle is \(A=\pi r^2\).
\(A_{circle}=\pi\times3^2=9\pi\mathrm{in}^2\approx9\times 3.14 = 28.26\mathrm{in}^2\)

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{square}-A_{circle}\)
\(A = 36 - 28.26=7.74\mathrm{in}^2\approx7.7\mathrm{in}^2\)

Answer:

\(7.7\mathrm{in}^2\)