Question

find the shaded area of the figure below. round your answer to the nearest tenth. all angles that look like right angles are right angles. do not round until the last step.

(image of a figure with a rectangle (12 ft height, 8 ft width) and a semicircle on top)

area = \boxed{} square units

Explanation:

Step1: Calculate rectangle area

$\text{Area}_{\text{rectangle}} = 8 \times 12 = 96$ square feet

Step2: Determine semicircle radius

$r = \frac{8}{2} = 4$ feet

Step3: Calculate semicircle area

$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times \pi \times 4^2 = 8\pi$ square feet

Step4: Sum the two areas

$\text{Total Area} = 96 + 8\pi$

Answer:

121.1 square units