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

Explanation:

Step1: Identify the components of the composite figure

The figure consists of three rectangles and one quarter-circle.

Step2: Calculate the area of the bottom-left rectangle

The dimensions are $4\text{ mi}$ by $3\text{ mi}$. $$A_1 = 4 \times 3 = 12\text{ sq mi}$$

Step3: Calculate the area of the middle rectangle

The width is $7 - 4 = 3\text{ mi}$. The height is $6 + 3 = 9\text{ mi}$. $$A_2 = 3 \times 9 = 27\text{ sq mi}$$

Step4: Calculate the area of the top-middle rectangle

The width is $3\text{ mi}$ and the height is $2\text{ mi}$. $$A_3 = 3 \times 2 = 6\text{ sq mi}$$

Step5: Calculate the area of the quarter-circle

The radius is $9\text{ mi}$. $$A_4 = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (9)^2 = \frac{81\pi}{4} \approx 63.617\text{ sq mi}$$

Step6: Sum the areas to find the total area

Add all calculated areas together. $$A_{total} = 12 + 27 + 6 + 63.617 = 108.617\text{ sq mi}$$

Step7: Round to the nearest hundredth

Round the final result. $$108.617 \approx 108.62$$

Answer:

108.62 square miles