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

Answer:

$110.27$ square kilometers

Explanation:

Step1: Identify the composite shapes

The figure consists of a rectangle and a quarter-circle.

Step2: Calculate the rectangle area

$$A_{rect} = 9 \text{ km} \times 8 \text{ km} = 72 \text{ km}^2$$

Step3: Determine the quarter-circle radius

$$r = 9 \text{ km} + 6 \text{ km} - 5 \text{ km} - 3 \text{ km} = 7 \text{ km}$$

Step4: Calculate the quarter-circle area

$$A_{qc} = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (7)^2 \approx 38.27 \text{ km}^2$$

Step5: Sum the total area

$$A_{total} = 72 + 38.27 = 110.27 \text{ km}^2$$