When a shape is reduced by a scale of \( k \), the area of the new shape is given by the formula:
\[ \text{New Area} = k^2 \times \text{Original Area} \]
In this case, the original area of the pentagon is 120 square inches and the scale factor \( k \) is 0.5.
Calculating the new area:
\[ \text{New Area} = (0.5)^2 \times 120 = 0.25 \times 120 = 30 , \text{in}^2 \]
Therefore, the area of the reduced pentagon is 30 in².