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 the side length of the hexagon

Since the perimeter of a regular hexagon is \(P = 6s\) (where \(s\) is the side - length) and \(P=7.5\) in. Then \(s=\frac{P}{6}\).
\(s=\frac{7.5}{6}=1.25\) in.

Step2: Analyze the length of the dotted line

The dotted line is composed of 3 side - lengths of the regular hexagon. Let \(L\) be the length of the dotted line. Then \(L = 3s\).
Substitute \(s = 1.25\) into the formula: \(L=3\times1.25\).
\(L = 3.75\) in.

Answer:

3.75 in.