Question

find the area of the yellow shaded region.
8 cm
area =? cm²
round to the nearest tenth.

Explanation:

Step1: Calculate the area of the square

The area formula of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 8\) cm, so \(A_{square}=8\times8 = 64\) \(cm^{2}\).

Step2: Calculate the area of the four quarter - circles (a whole circle)

The four quarter - circles together form a circle. The radius \(r\) of the circle is \(r=\frac{8}{2}=4\) cm. The area formula of a circle is \(A=\pi r^{2}\). Substituting \(r = 4\) cm, we get \(A_{circle}=\pi\times4^{2}=16\pi\approx16\times3.14 = 50.24\) \(cm^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A\) is the area of the square minus the area of the circle. So \(A=A_{square}-A_{circle}=64 - 50.24=13.76\approx13.8\) \(cm^{2}\).

Answer:

\(13.8\) \(cm^{2}\)