Question

what is the perimeter of the figure below? you may round your answer to two decimal places. (there is a sector with radius 7 ft and central angle 120°)

Explanation:

Step1: Find the length of the arc

The formula for the length of an arc is $L=\frac{\theta}{360^\circ}\times2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius. Here, $\theta = 360^\circ - 120^\circ=240^\circ$ and $r = 7$ ft.
So, $L=\frac{240^\circ}{360^\circ}\times2\pi\times7=\frac{2}{3}\times14\pi=\frac{28\pi}{3}\approx\frac{28\times3.1416}{3}\approx29.32$ ft.

Step2: Add the lengths of the two radii

The two radii each have length 7 ft, so their total length is $7 + 7 = 14$ ft.

Step3: Calculate the perimeter

The perimeter of the sector is the sum of the arc length and the two radii. So, perimeter $=29.32+14 = 43.32$ ft.

Answer:

43.32 ft