# Activities

• • • ##### Subject Area

• Math: Geometry: Triangles

• ##### Author 9-12

60 Minutes

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

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Report an Issue

Triangulation Problem

#### Activity Overview

In this Computer Algebra System (CAS) activity, students use 'landscape' paper and fold the top left corner of the page so that it just touches the bottom of the page. They calculate the area of the triangle formed by the bottom left corner and find the distance that forms a triangle with maximum area.

#### Before the Activity

• Install TI Connect™ using the TI connectivity cable
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 2 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Fold the top left corner of the landscape paper so that it just touches the bottom of the page
• Measure the sides of the resultant triangle and determine its area
• Fold the paper using the outlined method for different values
• Record the corresponding values for the base and for the area of the triangle
• Determine the value which gives the maximum area of the triangle
• Draw a scatter plot of the increment value against the area
• Use the graph to estimate the value which gives the maximum area of the triangle
• Determine an expression for the hypotenuse of the triangle
• Find the expression for the area of the triangle
• Calculate the derivative of the expression for the area
• Equate the derivative to zero and find the maximum area
• Generalize the solution
• #### After the Activity

Students answer questions on the Activity sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary