Question

1. scale factor = ____ (original hexagon with side 30 in, smaller hexagon with side 6 in)

Explanation:

Step1: Recall scale factor formula

The scale factor from the original figure to the scaled figure is the ratio of the length of the scaled figure to the length of the original figure. So, if \( L_{scaled} \) is the length of the scaled figure and \( L_{original} \) is the length of the original figure, the scale factor \( k=\frac{L_{scaled}}{L_{original}} \).

Step2: Identify the lengths

From the diagram, the length of the original hexagon is \( 30 \) in and the length of the scaled (smaller) hexagon is \( 6 \) in.

Step3: Calculate the scale factor

Substitute the values into the formula: \( k = \frac{6}{30} \). Simplify the fraction: \( \frac{6}{30}=\frac{1}{5}=0.2 \).

Answer:

\(\frac{1}{5}\) (or \(0.2\))