Question

find the area of the figure below, composed of a parallelogram and one semicircle. rounded to the nearest tenths place
14
12
8
answer attempt 1 out of 5
137.1
submit answer

Explanation:

Step1: Calculate area of parallelogram

The formula for the area of a parallelogram is \( A = base \times height \). Here, the base is 14 and the height is 8. So, \( A_{parallelogram} = 14 \times 8 = 112 \).

Step2: Calculate area of semicircle

The diameter of the semicircle is equal to the height of the parallelogram, which is 8. So the radius \( r = \frac{8}{2} = 4 \). The formula for the area of a full circle is \( A = \pi r^2 \), so the area of a semicircle is \( \frac{1}{2} \pi r^2 \). Substituting \( r = 4 \), we get \( A_{semicircle} = \frac{1}{2} \times \pi \times 4^2 = \frac{1}{2} \times \pi \times 16 = 8\pi \approx 8 \times 3.1416 = 25.1328 \).

Step3: Sum the areas

Add the area of the parallelogram and the area of the semicircle: \( Total\ Area = 112 + 25.1328 \approx 137.1328 \). Rounding to the nearest tenths place, we get 137.1.

Answer:

137.1