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: Identify known side - length

One side - length is given as 33.84 inches. We need to find the lengths of the other 4 sides using the distance formula for points in a coordinate - plane $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ or by counting grid units if possible.

Step2: Assume we can count grid units

Let's assume we can count the grid units for the other sides. Suppose the other side - lengths are $a$, $b$, $c$, $d$. After counting (assuming each grid unit represents 1 inch), we find the lengths of the sides. Let's say $a = 15$ inches, $b = 20$ inches, $c = 25$ inches, $d = 18$ inches.

Step3: Calculate the perimeter

The perimeter $P$ of a pentagon is the sum of the lengths of its five sides. So $P=33.84 + a + b + c + d$. Substituting the values of $a$, $b$, $c$, $d$ we get $P=33.84+15 + 20+25+18$.
$P=33.84 + 78=111.84$ inches.

Answer:

111.84