Question

the gazebo in the town square has a pentagonal roof, as shown. around the edges of the roof, the mayors staff is installing decorative rope lighting so that the gazebo can be used for nighttime events. what length of rope lighting do they need to outfit the entire roof edge? enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the pentagon: inches

Explanation:

Step1: Recall perimeter formula

Perimeter of a polygon is sum of side - lengths.

Step2: Identify known side - length

One side - length is given as 33.84 inches. But we need to find lengths of other 4 sides using distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. However, since the graph is not fully clear on all the vertices' coordinates for the other sides, assume we have all side - lengths measured and add them up. Let the side - lengths be $a,b,c,d,e$. Here $a = 33.84$. If we assume we find the other 4 side - lengths and add them together.
Let the lengths of the other 4 sides be $s_1,s_2,s_3,s_4$. The perimeter $P=a + s_1+s_2+s_3+s_4$.

Answer:

(We need more information about the other side - lengths from the graph to give a numerical answer. But the process to find the perimeter is to sum all 5 side - lengths of the pentagon.)