Home > MC2 > Chapter 10 > Lesson 10.1.1 > Problem10-11

10-11.

The two pentagons below are similar.

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

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

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

2. What is the scale factor between their areas?

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

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?

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

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

$26.67$ cm$^{2}$