The two pentagons below are similar.

1. What is the scale factor between their side lengths?

   Help (a):

   Compare the ratio of two of the given corresponding sides from the old to the new shape. What do you get?

   Answer (a):

   $\frac{6}{9} = \frac{4}{6} = \frac{2}{3}$

2. What is the scale factor between their areas?

   Hint (b):

   The area ratio is $\frac{\text{new area}}{\text{original area}} = ( \text{scale factor} )^2$

   Help (b):

   If the scale factor is $\frac{2}{3}$, what would the area ratio be?

3. If the original shape has an area of $60$ square centimeters, what is the area of the new shape?

   Help (c):

   Use the area ratio you found in part (b) to determine the area of the new shape.

   Hint (c):

   Multiply original area by the area ratio to get new area.

   Answer (c):

   $26.67$ cm^{$^{2}$}