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)

Question

Responses

54 in.2
54 in. squared

1,458 in.2
1,458 in. squared

18 in.2
18 in. squared

162 in.

Answer 1

When a three-dimensional shape is dilated by a scale factor \( k \), the surface area of the shape is multiplied by \( k^2 \).

In this case, the scale factor is \( 13 \), so we will calculate the new surface area as follows:

1. Calculate \( k^2 \): \[ k^2 = 13^2 = 169 \]

2. Multiply the original surface area by \( k^2 \): \[ \text{New Surface Area} = \text{Original Surface Area} \times k^2 = 486 \text{ in}^2 \times 169 \]

   Now, calculate \( 486 \times 169 \): \[ 486 \times 169 = 82,194 \text{ in}^2 \]

So, the new surface area after dilating the triangular prism would be \( 82,194 \text{ in}^2 \).

However, it appears that this was not one of the options provided. Please check the scale factor and surface area calculations if the problem requires specific values.