Question
The pentagon below has been reduced by a scale of 0.5.
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
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
Answers
GPT-4o mini
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**.
\[
\text{New Area} = k^2 \times \text{Original Area}
\]
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**.