Question

similar figures and area quick check
determine how dilation affects the area of a pentagon when the sides of the pentagon are dilated by a scale factor less than 1. (1 point)

• the area decreases, but less rapidly than the lengths of the sides decrease.
• the area increases more rapidly than the lengths of the sides increase.
• the area decreases more rapidly than the lengths of the sides decrease.
• the area increases, but less rapidly than the lengths of the sides increase

Explanation:

When a figure is dilated by a scale factor \( k \), the ratio of the areas of the dilated figure to the original figure is \( k^2 \) (for similar figures, area scales with the square of the linear scale factor). If the scale factor \( k \) is less than 1 (e.g., \( k = 0.5 \)), the linear dimensions (side lengths) decrease by a factor of \( k \), but the area decreases by a factor of \( k^2 \). Since \( k^2

Answer:

The area decreases more rapidly than the lengths of the sides decrease.