Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Surface Area and Volume

9-12

7 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• ##### Software

Cabri Geometry™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
If you don't have the Cabri® application, you may use a pencil or paper.

## Finding the area of a perfect polygon.

#### Activity Overview

To find the area of a "regular polygon."

#### Before the Activity

geometry FLIO
areaofap STDY
georevie.ratios FIG (if you have the Cabri app) or, Pictureperfect.JPG.

#### During the Activity

1.)With Cabri® 2.)Without Cabri® Lets start the starting points now for Cabri®: To get a 'feel' of starting points, you should download the Notefolio Application and the TI StudyCards™ Application if not already. Go ahead and download the "STDY areaofap" and "FLIO geonotes" will tell you several important factors of polygons...After you have read both you must download the "FIG ratio" Now with your Cabri® Application, upload the ratiofigure in your new folder named georevie. Observe the diagram, one of the triangle is a 30-60-90 triangle which only occurs with a hexagon.
Now there may be other measures such as 72 for the pentagon, but you can figure that out by reading geonotes. In this case we will say that segment BC is ten units.
That is really all we need, we could also use the radius or the apothem, but hey...it is already given... Non-Cabri Users: Download the picture or bitmap named Pictureperfect. It shows what the person with Cabri will see.
You should have Notefolio and TI StudyCards™...so why bother?

#### After the Activity

Now we have a choice of Trig Ratios: tangent:apothem/half side sine:half side/radius cosine:apothem/radius. Now you have a choice to which variables and notations are available. Don't bother with sine because you are not really trying to find the radius...right? IN SET CASE (REFER TO LAST) half side-5 radius=need not know apothem=? So we can now use tangent in this case. tangent(60)=5/apothem... Figure that out and whola...you found the apothem. Leave the apotem in simplest radical form if you need to. In this case it should be five square root three. Now the perimeter is all the sides added together... Now the formula is A=(1/2)Pa, having A area, P perimeter, and a apothem. Plug-in the variables and whola...the area of a regular polygon.