Question

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)
Responses

The area decreases, but less rapidly than the lengths of the sides decrease.
The area decreases, but less rapidly than the lengths of the sides decrease.

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

The area increases more rapidly than the lengths of the sides increase.
The area increases more rapidly than the lengths of the sides increase.

The area increases, but less rapidly than the lengths of the sides increase.
The area increases, but less rapidly than the lengths of the sides increase.

Answer 1

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

Reason: If side lengths scale by k (0<k<1), areas scale by k^2, and for 0<k<1 we have k^2 < k, so the area shrinks faster than the side lengths.