Question
Question A triangular prism has a surface area of 486 in.2 . If it were dilated using a scale factor of 13 , what would the new surface area be?(1 point) Responses 162 in.2 162 in. squared 1,458 in.2 1,458 in. squared 54 in.2 54 in. squared 18 in.2
Answers
Answered by
GPT-4o mini
To find the new surface area of the triangular prism after dilation with a scale factor, you can use the following relationship: when a shape is dilated by a scale factor \( k \), the surface area changes by a factor of \( k^2 \).
Given:
- Original surface area = 486 in²
- Scale factor \( k = 13 \)
First, calculate \( k^2 \):
\[
k^2 = 13^2 = 169
\]
Next, multiply the original surface area by \( k^2 \):
\[
\text{New surface area} = \text{Original surface area} \times k^2 = 486 \, \text{in}^2 \times 169
\]
Calculating that:
\[
486 \times 169 = 82,194 \, \text{in}^2
\]
So the new surface area after dilation would be:
\[
\text{New surface area} = 82,194 \, \text{in}^2
\]
None of the provided responses are correct based on the calculation above. Please double-check the problem statement or the options provided.
Given:
- Original surface area = 486 in²
- Scale factor \( k = 13 \)
First, calculate \( k^2 \):
\[
k^2 = 13^2 = 169
\]
Next, multiply the original surface area by \( k^2 \):
\[
\text{New surface area} = \text{Original surface area} \times k^2 = 486 \, \text{in}^2 \times 169
\]
Calculating that:
\[
486 \times 169 = 82,194 \, \text{in}^2
\]
So the new surface area after dilation would be:
\[
\text{New surface area} = 82,194 \, \text{in}^2
\]
None of the provided responses are correct based on the calculation above. Please double-check the problem statement or the options provided.