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)

Question

Responses

915.9 in.2
915.9 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

305.3 in.2

Answer 1

When a figure is dilated by a scale factor \( k \), the surface area of the dilated figure is proportional to the square of the scale factor. This means:

\[ \text{Surface Area of Dilated Figure} = k^2 \times \text{Surface Area of Original Figure} \]

In this case, the scale factor \( k \) is 6, so \( k^2 = 6^2 = 36 \).

Given that the surface area of the dilated figure is 10,990.8 in², we can set up the equation:

\[ 10,990.8 = 36 \times \text{Surface Area of Original Figure} \]

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

\[ \text{Surface Area of Original Figure} = \frac{10,990.8}{36} \approx 305.3 , \text{in}^2 \]

Therefore, the surface area of the original figure is approximately 305.3 in².

So the correct response is:

305.3 in.².