A rectangle with area 12 square units is dilated by a scale factor of \(k\). Find the area of the image for each given value of \(k\).

1. \(k=2\)
2. \(k=5\)
3. \(k=1\)
4. \(k=\frac14\)
5. \(k=1.2\)

The area of a circle of radius 1 is \(\pi\) units squared. Use scaling to explain why the area of a circle of radius \(r\) is \(\pi r^2\) units squared.

Trapezoid \(A’B’C’D\) was created by dilating trapezoid \(ABCD\) using \(D\) as the center of dilation.

A large trapezoid A'B'C'D' comprised of smaller shapes on a grid. The blue shape ABCD is a smaller trapezoid. Triangle Q in top right corner. Quadrilateral P in lower right corner. 

1. What was the scale factor of the dilation?
2. Based on the scale factor, how many copies of \(ABCD\), including the original, should fit inside \(A’B’C’D\)?
3. How can you see your answer to these questions in the diagram?