Question

find the area of the figure below, composed of a rectangle and a semicircle. round to the nearest tenths place.

Explanation:

Step1: Calculate area of rectangle

The formula for the area of a rectangle is \( A_{rectangle} = length \times width \). Here, length is 7 and width is 4. So, \( A_{rectangle} = 7 \times 4 = 28 \).

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 \( A_{semicircle} = \frac{1}{2} \pi (2)^2 = \frac{1}{2} \pi \times 4 = 2\pi \approx 2 \times 3.1416 = 6.2832 \).

Step3: Calculate total area

Add the area of the rectangle and the area of the semicircle. \( A_{total} = A_{rectangle} + A_{semicircle} = 28 + 6.2832 = 34.2832 \).

Step4: Round to nearest tenth

Rounding 34.2832 to the nearest tenth, we look at the hundredth place (8), which is greater than 5, so we round up the tenth place. So, 34.3.

Answer:

34.3