A triangular prism has a surface area of 486 in.2 . If it were dilated using a scale factor of 1/3 , 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.2
162 in. squared

Answer 1

When a shape is dilated using a scale factor, the surface area changes by the square of that scale factor.

In this case, the scale factor is \( \frac{1}{3} \). To find the new surface area, we can apply the scale factor to the original surface area of 486 in².

1. First, find the square of the scale factor: \[ \left(\frac{1}{3}\right)^2 = \frac{1}{9} \]

2. Then multiply the original surface area by this value: \[ \text{New Surface Area} = \text{Original Surface Area} \times \frac{1}{9} \] \[ \text{New Surface Area} = 486 \times \frac{1}{9} = 54 \text{ in.}^2 \]

Thus, the new surface area after dilation is \( 54 \text{ in.}^2 \).

The correct response is 54 in.².