# Activities

• • • ##### Subject Area

• Math: Geometry: Quadrilaterals and Polygons

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 10 from the EXPLORATIONS Book:
Shaping Middle Grades Mathematics: Activities for Geoboard and the TI-73

• ##### Report an Issue

Get to the Point! Coordinate Geometry!

#### Activity Overview

In this activity, students use the Geoboard to determine the area of any polygon using coordinates.

#### Before the Activity

• Start the Geoboard App and format it
• See the attached PDF file for detailed instructions for this activity
• Print pages 113 - 118 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

Follow the Activity procedures:

• Construct a heptagon using the coordinates of its vertices
• Starting at any point and moving counterclockwise around the polygon, list the vertices in a vertical column in consecutive order
• Repeat the starting point at the bottom of the list
• Calculate D, the sum of the down diagonal products, and U, the sum of the up diagonal products
• Determine the area of the polygon which is one-half of the difference between D and U

• Construct a square, draw a diagonal, and a line segment that divides the square into four non overlapping regions
• Find the ratios of the areas of the four regions
• #### After the Activity

Students complete the Activity sheet and answer questions.

Review student results:

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