what is the area of this figure?\n\nif necessary, round your answer to the nearest hundredth.\n\nsquare inches

Explanation:

Step1: Identify the components of the composite figure

The figure consists of a rectangle and a semicircle.

Step2: Calculate the diameter of the semicircle

Sum the vertical segments on the left side: $4\text{ in} + 8\text{ in} + 2\text{ in} = 14\text{ in}$.

Step3: Calculate the area of the semicircle

Use the formula $A_{semi} = \frac{1}{2} \pi r^2$ where $r = \frac{14}{2} = 7$. $$A_{semi} = \frac{1}{2} \pi (7)^2 = 24.5\pi \approx 76.969\text{ in}^2$$

Step4: Calculate the area of the rectangular sections

The figure can be split into a $3 \times 2$ rectangle and a $14 \times 4$ rectangle. $$A_{rect} = (3 \times 2) + (14 \times 4) = 6 + 56 = 62\text{ in}^2$$

Step5: Sum the areas for the total area

Add the area of the rectangles and the semicircle. $$A_{total} = 62 + 76.969 = 138.969\text{ in}^2$$

Step6: Round to the nearest hundredth

Round the final result to two decimal places. $$138.969 \approx 138.97$$

Answer:

138.97 square inches