Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long. She then takes a photo of the sandbox and prints the photo. In photo of the sandbox and prints the photo, the sides of the hexagon are each 4 inches long. Identify the scale factor that was used to create the printed photo of the sandbox. Express your answer as a decimal

1 answer

To find the scale factor used to create the printed photo of the sandbox, we start by comparing the original dimensions of the sandbox to the dimensions in the printed photo.

The original sandbox is a regular hexagon with each side measuring 40 inches. The printed photo depicts the same hexagon but with each side measuring 4 inches.

To find the scale factor, we can use the formula for scale factor:

\[ \text{Scale Factor} = \frac{\text{Length in Photo}}{\text{Original Length}} \]

Substituting the given values:

\[ \text{Scale Factor} = \frac{4 \text{ inches}}{40 \text{ inches}} = \frac{4}{40} = \frac{1}{10} \]

To express this as a decimal:

\[ \frac{1}{10} = 0.1 \]

Thus, the scale factor used to create the printed photo of the sandbox is

\[ \boxed{0.1} \]