Activity: The Far Fetched Areas Glitch Problem

Far Fetched Scientific Inc.
Fargo, North Dakota

Dear fellow geometry student,

I have a problem that I hope you can help me with. We here at Far Fetched sell tiles of different designs. We charge by the square inch ($1.00). In order to find out the area we need to make a drawing of our tiles and then use a program called the Geometer’s Sketchpad to tell us how many square centimeters there are in our tiles. Here is one of our rectangular tiles.

1. First we draw a rectangle. You will find one just like the one above if you load the file rectangle1.gsp
2. Measure the sides by clicking on (and highlighting) them. Click on AB. You should notice two “handles” appear on the line. Go to the Measure menu and choose segment. You should get the measurement of AB.
3. Repeat the same for BC.

On the same sketch you will also see a square tile. This tile is called a square inch because each side of the square is one inch.

Our usual way is to click on (and highlight) the polygon interior and then choose Area from the Measure menu. But for some reason the area measure tool doesn’t work. We heard you have some ways of finding the area without using the measure area menu option. We need your help in finding the areas of the shapes on the other page.

I will be eternally grateful for your help!

Sincerely yours,

I. M. Farout
CEO, Far Fetched Inc.

PS See if you can help us with circular shapes as well.

if you have figured out how to find the area of a rectangle how about some of these shapes that you will be using in our pattern blocks designs?

Here's another way to make these designs with a Java Applet.