Question

find the area of the blue shaded region.
10 cm
8 cm
3 cm
a = ? cm²
round your answer to the nearest hundredth.

Explanation:

Step1: Calculate area of rectangle

The rectangle has length \( 10 \, \text{cm} \) and width \( 8 \, \text{cm} \). The area of a rectangle is \( \text{length} \times \text{width} \), so \( A_{\text{rectangle}} = 10 \times 8 = 80 \, \text{cm}^2 \).

Step2: Calculate area of circle

The circle has radius \( r = 3 \, \text{cm} \). The area of a circle is \( \pi r^2 \), so \( A_{\text{circle}} = \pi \times 3^2 = 9\pi \approx 28.2743 \, \text{cm}^2 \).

Step3: Subtract circle area from rectangle area

The shaded area is the area of the rectangle minus the area of the circle: \( A_{\text{shaded}} = A_{\text{rectangle}} - A_{\text{circle}} = 80 - 9\pi \approx 80 - 28.2743 = 51.7257 \, \text{cm}^2 \). Rounding to the nearest hundredth gives \( 51.73 \, \text{cm}^2 \).

Answer:

\( 51.73 \)