Lesson 6

Explore

 

Does doubling the dimensions of an object double its area? Many people think it does. But as Kunal learned, this is not true! As you discovered in the Math Lab, when a scale factor (k) is applied to a 2-D shape, it creates a similar shape. The area of the similar shape (A2) is the product of the square of the scale factor (k2) and the area of the original shape (A1). We could write this as:

 

area of similar 2-D shape = k2 × area of the original shape

 

 

or

 

A2 = k2 × A1

 

Rearranging this formula allows you to determine the square of the scale factor that relates two similar 2-D shapes.

 

 

By taking the square root of the area of a shape divided by the area of the original shape, you can determine the scale factor.