Question

A dilated figure has a surface area of 10,990.8 in.2
. The figure was dilated by a scale factor of 6. What is the surface area of the original figure?(1 point)
Responses

1,831.8 in.2
1 comma 831 point 8 in. squared

395,668.8 in.2
395 comma 668 point 8 in. squared

305.3 in.2
305.3 in. squared

915.9 in.2

Answer 1

When a figure is dilated by a scale factor \( k \), the surface area of the new figure is given by the formula:

\[
\text{New Surface Area} = k^2 \times \text{Original Surface Area}
\]

In your case, the dilated surface area is \( 10,990.8 \, \text{in}^2 \) and the scale factor \( k = 6 \).

We can rearrange the formula to find the original surface area:

\[
\text{Original Surface Area} = \frac{\text{New Surface Area}}{k^2}
\]

Now, calculate \( k^2 \):

\[
k^2 = 6^2 = 36
\]

Now substitute into the formula:

\[
\text{Original Surface Area} = \frac{10,990.8}{36}
\]

Calculating that gives:

\[
\text{Original Surface Area} = 305.3 \, \text{in}^2
\]

So, the surface area of the original figure is:

**305.3 in.²**