Question

12 find the area of the shaded region. round to the nearest hundredths place if necessary. 8 cm area =

Explanation:

Step1: Find area of circle

The square has side 8 cm. The diagonal of the square is the diameter of the circle. For a square with side \( s \), diagonal \( d = s\sqrt{2} \), so \( d = 8\sqrt{2} \) cm. Radius \( r=\frac{d}{2}=4\sqrt{2} \) cm. Area of circle \( A_{circle}=\pi r^{2}=\pi(4\sqrt{2})^{2}=\pi\times32\approx32\times3.1416 = 100.53 \) \( cm^{2} \) (using \( \pi\approx3.1416 \)).

Step2: Find area of square

Area of square \( A_{square}=s^{2}=8^{2}=64 \) \( cm^{2} \).

Step3: Find shaded area

Shaded area = Area of circle - Area of square. So \( 100.53 - 64 = 36.53 \) \( cm^{2} \) (rounded to nearest hundredth).

Answer:

\( 36.53 \) square centimeters (or \( 36.53\space cm^{2} \))