Question

what is the perimeter of the figure below?
you may round your answer to two decimal places.

Explanation:

Step1: Find the length of the arc

The formula for the length of an arc is $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle and $r$ is the radius. Here, $\theta = 360^\circ - 120^\circ = 240^\circ$ and $r = 30$ ft.
So, $L = \frac{240^\circ}{360^\circ} \times 2\pi \times 30$.
Simplify: $L = \frac{2}{3} \times 60\pi = 40\pi$ ft.

Step2: Add the lengths of the two radii

The two radii each have length 30 ft, so their total length is $30 + 30 = 60$ ft.

Step3: Calculate the perimeter

The perimeter of the figure is the sum of the arc length and the two radii. So, Perimeter = $40\pi + 60$.
Calculate the numerical value: $40\pi \approx 40 \times 3.1416 = 125.664$, then $125.664 + 60 = 185.664$ ft. Rounding to two decimal places, it's approximately 185.66 ft.

Answer:

The perimeter of the figure is approximately $\boxed{185.66}$ feet.