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 \(A_{square}=s^2\), where \(s = 5\) ft.
\(A_{square}=5\times5=25\) \(ft^{2}\)

Step2: Calculate the area of the circle

The diameter of the circle \(d = 5\) ft, so the radius \(r=\frac{d}{2}=\frac{5}{2}=2.5\) ft. The area formula for a circle is \(A_{circle}=\pi r^{2}\).
\(A_{circle}=\pi\times(2.5)^{2}=\pi\times6.25\approx3.14\times6.25 = 19.625\) \(ft^{2}\)

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{square}-A_{circle}\)
\(A=25 - 19.625=5.375\approx5.4\) \(ft^{2}\)

Answer:

\(5.4\) \(ft^{2}\)