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

915.9 in.2
915.9 in. squared

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

Answer 1

To find the surface area of the original figure before dilation, we can use the relationship between the surface area of similar figures and the scale factor.

If a figure is dilated by a scale factor of \( k \), 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 \( k = 6 \), and the surface area of the dilated figure is \( 10,990.8 \) in². We can set up the equation:

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

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now, substituting this into the equation:

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

To find the surface area of the original figure, we divide both sides by 36:

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

Calculating the right-hand side:

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

Thus, the surface area of the original figure is:

**305.3 in²**