Lesson 6

Lesson 6 Summary

 

Unlike some cartoon characters, scale diagrams require dimensions and areas that are proportional. This ensures that the enlarged or reduced shapes are similar to the original ones. The dimensions of similar 2-D shapes are related by a scale factor.

 

A common misconception is that the area of two similar shapes is also related by the scale factor. But as you discovered in your Math Lab, the area of two similar shapes are related by the square of the scale factor (k2). The area of the similar shape is the product of the square of the scale factor (k2) and the area of the original shape.

 

area of similar 2-D shape = k2 (area of original shape)

 

You can rearrange this formula to isolate the square of the scale factor that relates the two similar 2-D shapes.

 

 

The scale factor can be determined by taking the square root of the area of a shape divided by the area of the original shape.

 

 

In Lesson 7 you will investigate the relationship between the scale factor and the surface area of two similar 3-D objects and the relationship between the scale factor and the volumes of two similar objects.