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)

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

1 answer

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.