what is the area of this figure?\nif necessary, round your answer to the nearest hundredth.
what is the area of this figure?\nif necessary, round your answer to the nearest hundredth.
Answer
Explanation:
Step1: Identify the components of the figure
The figure consists of a quarter-circle, a large rectangle, and a small rectangle.
Step2: Calculate the area of the quarter-circle
The radius $r$ is $6\text{ mi}$. $$A_{circle} = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (6)^2 = 9\pi \approx 28.2743\text{ sq mi}$$
Step3: Calculate the area of the large rectangle
The width is $3\text{ mi}$ and the height is $12\text{ mi}$. $$A_{rect1} = 3 \times 12 = 36\text{ sq mi}$$
Step4: Calculate the area of the small rectangle
The width is $2\text{ mi}$ and the height is $3\text{ mi}$. $$A_{rect2} = 2 \times 3 = 6\text{ sq mi}$$
Step5: Sum the areas for the total area
Total Area $= A_{circle} + A_{rect1} + A_{rect2}$ $$A_{total} = 28.2743 + 36 + 6 = 70.2743\text{ sq mi}$$
Step6: Round to the nearest hundredth
Round $70.2743$ to two decimal places. $$A_{total} \approx 70.27\text{ sq mi}$$
Answer:
70.27 square miles