Question

fiona must find the length indicated by the dotted line for the tiles she is installing. she knows that each polygon is a regular hexagon with a perimeter of 7.5 in. what is the length of the dotted line? round to the nearest hundredth. 2.50 in 3.75 in 5.00 in 6.25 in

Explanation:

Step1: Find side - length of hexagon

A regular hexagon has 6 equal sides. Given perimeter $P = 7.5$ in. Let the side - length be $s$. Using the formula $P=6s$, we can solve for $s$: $s=\frac{P}{6}=\frac{7.5}{6}=1.25$ in.

Step2: Analyze the dotted - line length

The dotted line in the figure is composed of 3 side - lengths of the regular hexagons. So the length $L$ of the dotted line is $L = 3s$.
Substitute $s = 1.25$ in into the formula: $L=3\times1.25 = 3.75$ in.

Answer:

3.75 in