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 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

Answer 1

When a figure is dilated by a scale factor, the surface area of the dilated figure is proportional to the square of the scale factor.

Given:

• Dilated surface area = 10,990.8 in²
• Scale factor = 6

To find the original surface area, we can use the formula:

\[ \text{Dilated Surface Area} = \text{Original Surface Area} \times (\text{Scale Factor})^2 \]

In this case:

\[ 10,990.8 = \text{Original Surface Area} \times (6^2) \] \[ 10,990.8 = \text{Original Surface Area} \times 36 \]

Now, to find the original surface area, divide both sides by 36:

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

Thus, the surface area of the original figure is 305.3 in².