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

305.3 in.2
305.3 in. squared

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

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

915.9 in.2
915.9 in. squared

Answer 1

To find the surface area of the original figure before dilation, we can use the relationship between the scale factor and surface area. When a figure is dilated by a scale factor \( k \), the surface area of the dilated figure is given by:

\[
\text{Surface Area}_{\text{dilated}} = k^2 \times \text{Surface Area}_{\text{original}}
\]

In this case, the scale factor \( k = 6 \). The surface area of the dilated figure is \( 10,990.8 \, \text{in}^2 \). We can set up the equation:

\[
10,990.8 = 6^2 \times \text{Surface Area}_{\text{original}}
\]

Calculating \( 6^2 \):

\[
6^2 = 36
\]

So the equation becomes:

\[
10,990.8 = 36 \times \text{Surface Area}_{\text{original}}
\]

Now, we can solve for the surface area of the original figure:

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

Calculating this gives:

\[
\text{Surface Area}_{\text{original}} \approx 305.3 \, \text{in}^2
\]

Thus, the surface area of the original figure is **305.3 in.²**.