# Lesson 5

Scaling and Unscaling

- Let’s examine the relationships between areas of dilated figures and scale factors.

### Problem 1

A circle with an area of \(8\pi\) square centimeters is dilated so that its image has an area of \(32\pi\) square centimeters. What is the scale factor of the dilation?

2

4

8

16

### Problem 2

A trapezoid has an area of 100 square units. What scale factor would be required to dilate the trapezoid to have each area?

- 6400 square units
- 900 square units
- 100 square units
- 25 square units
- 4 square units

### Problem 3

A triangle has an area of 6 square inches and a perimeter of 12 inches. Suppose it is dilated by some scale factor, and the area and perimeter of the image are calculated. Match each graph with the relationship it represents.

### Problem 4

A polygon with area 10 square units is dilated by a scale factor of \(k\). Find the area of the image for each value of \(k\).

- \(k=4\)
- \(k=1.5\)
- \(k=1\)
- \(k=\frac13\)

### Problem 5

Parallelogram \(AB’C’D'\) was obtained by dilating parallelogram \(ABCD\) using \(A\) as the center of dilation.

- What was the scale factor of the dilation?
- How many congruent copies of \(ABCD\) have we fit inside \(AB’C’D'\)?
- How does the area of parallelogram \(AB'C'D'\) compare to parallelogram \(ABCD\)?
- If parallelogram \(ABCD\) has area 12 square units, what is the area of parallelogram \(AB'C'D'\)?

### Problem 6

Select **all** solids whose cross sections are dilations of some two-dimensional shape using a point directly above the shape as a center and scale factors ranging from 0 to 1.

cylinder

cube

triangular prism

cone

triangular pyramid

### Problem 7

Select **all** expressions which give the measure of angle \(A\).

\(\arccos\left(\frac{28}{53}\right)\)

\(\arccos\left(\frac{45}{53}\right)\)

\(\arcsin\left(\frac{28}{53}\right)\)

\(\arcsin\left(\frac{45}{53}\right)\)

\(\arctan\left(\frac{28}{45}\right)\)

\(\arctan\left(\frac{45}{28}\right)\)