The pentagon below has been reduced by a scale of 0.5.

Question

A pentagon with an area of 120 inches squared.

What is the area of the reduced pentagon?
30 in.²
60 in.²
90 in.²
120 in.²

Answer 1

When a shape is reduced by a scale factor, its area is reduced by the square of that scale factor. In this case, the scale factor is 0.5.

To find the new area, you multiply the original area by the square of the scale factor:

\[ \text{New Area} = \text{Original Area} \times (\text{Scale Factor})^2 \]

Substituting the values:

\[ \text{New Area} = 120 , \text{in}^2 \times (0.5)^2 \] \[ \text{New Area} = 120 , \text{in}^2 \times 0.25 \] \[ \text{New Area} = 30 , \text{in}^2 \]

Therefore, the area of the reduced pentagon is 30 in².