Question

find the area of the yellow shaded region. area =? in² 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.
\(A_{square}=6\times6 = 36\) \(in^{2}\)

Step2: Calculate the area of the two - semicircles (which is equivalent to the area of one full circle)

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

Step3: Calculate the area of the shaded region

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

Answer:

\(7.7\)