D. Scale Factor and Area

You have worked with scale factors to determine unknown lengths. Can you also work with scale factors to determine unknown areas?

To determine the scale factor of similar shapes, we calculate the ratio of a side length on the scale diagram to the corresponding side length on the original shape.

Refer once again to the Scale Factor, Perimeter, and Area of a 2-D Shape applet (20 April 2013, Created with GeoGebra).

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


Note that as the scale factor increases, the length of both sides of the resulting shape increase accordingly.

When working with area (for example a rectangle, where A = lw), the scale factor applies to both dimensions (length and width). This means the scale factor must be squared to compare the areas of similar shapes.

Let's continue with an example that uses a scale factor and area.

Example 1

Recall these similar rectangles from the previous Practice Run.

The scale factor of the similar shapes is 3, determine the area of the enlargement.

Determine the area of the original.

Determine the area of the enlargement.
Multiply the area of the original shape by the scale factor squared.

Verify the area of the enlargement.
The scale factor is 3 (given) and the missing side length of the enlargement was determined in the Practice Run to be 2.1.