Describe how to solve problems for the area of a reduced or enlarged figure when the scale factor and dimensions of the original figure are given.

We are going to define the following variables:

A: Area of the original figure.

k: scale factor.

We have that the area of the new figure (reduced or enlarged, depends on the value of k) is:

A ' = k ^ 2 * A

Example: rectangle of dimensions (2) * (3) A factor of k = 2 is extended. Find the new area.

The original area is:

A = (2) * (3) = 6

The new area will be:

A ' = (2 * 2) * (2 * 3) = 4 * 6 = 24

Or equivalently:

A ' = k ^ 2 * A

A ' = (2) ^ 2 * (6) = 4 * 6 = 24

To solve problems for the area of a reduced or enlarged figure, first square the scale factor. Then use the given dimensions to find the area of the original figure. Multiply the square of the scale factor by the area of the original to get the reduced or enlarged figure.