Question

find the area of the figure below, composed of a rectangle and a semicircle. round to the nearest tenths place.
6
4
answer attempt 2 out of 3

Explanation:

Step1: Calculate area of rectangle

The formula for the area of a rectangle is \( A_{rectangle} = length \times width \). Here, length is 6 and width is 4. So, \( A_{rectangle} = 6 \times 4 = 24 \).

Step2: Calculate area of semicircle

The diameter of the semicircle is equal to the width of the rectangle, which is 4. So, the radius \( r = \frac{4}{2} = 2 \). The formula for the area of a full circle is \( A_{circle} = \pi r^2 \), so the area of a semicircle is \( A_{semicircle} = \frac{1}{2} \pi r^2 \). Substituting \( r = 2 \), we get \( A_{semicircle} = \frac{1}{2} \pi (2)^2 = 2\pi \approx 6.283 \).

Step3: Sum the areas

Add the area of the rectangle and the area of the semicircle: \( A_{total} = 24 + 2\pi \approx 24 + 6.283 = 30.283 \). Rounding to the nearest tenths place, we get \( 30.3 \).

Answer:

\( 30.3 \)