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

Explanation:

Step1: Identify the components of the figure

The figure consists of a semicircle on top of a composite rectangular base.

Step2: Calculate the diameter of the semicircle

The total width of the base is the sum of the horizontal segments. $$d = 2\text{ m} + 3\text{ m} + 7\text{ m} = 12\text{ m}$$

Step3: Calculate the radius of the semicircle

$$r = \frac{d}{2} = \frac{12}{2} = 6\text{ m}$$

Step4: Calculate the area of the semicircle

$$A_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (6)^2 = 18\pi \approx 56.5487\text{ m}^2$$

Step5: Calculate the area of the rectangular base

Divide the base into three vertical rectangles: $2 \times 0$ (not applicable), $3 \times (5-3) = 3 \times 2$, and $7 \times 5$. Alternatively, subtract the missing "steps" from a large $12 \times 5$ rectangle. $$A_{base} = (12 \times 5) - (2 \times 3) - (5 \times 2) = 60 - 6 - 10 = 44\text{ m}^2$$

Step6: Calculate the total area

$$A_{total} = A_{semicircle} + A_{base} = 56.5487 + 44 = 100.5487\text{ m}^2$$

Step7: Round to the nearest hundredth

$$A_{total} \approx 100.55\text{ m}^2$$

Answer:

100.55 square meters