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 305.3 in.2 305.3 in. squared 395,668.8 in.2 395 comma 668 point 8 in. squared 915.9 in.2

Answer 1

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

Let:
- \( S_d \) = surface area of the dilated figure = 10,990.8 in²
- \( S_o \) = surface area of the original figure
- \( k \) = scale factor = 6

The relationship is given by:

\[
S_d = k^2 \times S_o
\]

Substituting the values we know:

\[
10,990.8 = 6^2 \times S_o
\]
\[
10,990.8 = 36 \times S_o
\]

Now, to find \( S_o \), divide both sides by 36:

\[
S_o = \frac{10,990.8}{36}
\]
\[
S_o = 305.3 \text{ in}^2
\]

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