what is the area of this figure?\n\nif necessary, round your answer to the nearest hundredth.\n\nsquare…
what is the area of this figure?\n\nif necessary, round your answer to the nearest hundredth.\n\nsquare millimeters
Answer
Answer:
$96.27$ square millimeters
Explanation:
Step1: Divide figure into three basic shapes
The figure consists of two rectangles and one quarter-circle.
Step2: Calculate top rectangle area
$$A_{1} = 2 \text{ mm} \times 2 \text{ mm} = 4 \text{ mm}^{2}$$
Step3: Calculate middle rectangle area
$$A_{2} = (2 + 4) \text{ mm} \times 7 \text{ mm} = 6 \text{ mm} \times 7 \text{ mm} = 42 \text{ mm}^{2}$$
Step4: Identify quarter-circle radius
$$r = 4 + 2 + 2 = 8 \text{ mm}$$
Step5: Calculate quarter-circle area
$$A_{3} = \frac{1}{4} \pi r^{2} = \frac{1}{4} \pi (8)^{2} = 16\pi \approx 50.265 \text{ mm}^{2}$$
Step6: Sum areas and round result
$$A_{total} = 4 + 42 + 50.265 = 96.265 \approx 96.27 \text{ mm}^{2}$$