A figure's area changes by the square of the component that causes it to dilate. Consequently, the area will vary by a factor of 6 squared, or 36, if a figure is dilated by a factor of 6.
Dilation is a geometric transformation that enlarges or reduces a figure by a certain scale factor while maintaining its shape and proportionality.
When a figure is dilated by a factor, the linear dimensions (such as length, width, and height) are all multiplied by that factor.
Consequently, the relationship between the original area (A) and the dilated area (A') can be expressed as A' = k^2 * A, where k is the dilation factor.
In your example, with a dilation factor of 6, the area of the dilated figure would be 6^2 = 36 times the original area.
This is because both the length and the width are multiplied by 6, resulting in an overall scaling factor of 6 * 6 = 36 for the entire area.
Consider a simple case where the original figure has an area of 5 square units.
Applying the dilation factor of 6, the area of the dilated figure would be 5 * 36 = 180 square units.
This illustrates the quadratic relationship between the dilation factor and the change in area, highlighting how dilation affects the size of a figure in a non-linear manner.