Shape 

Copyright David & Cynthia Thomas, 2009

Area of Triangles--Directed Activity: Perimeter vs. Area

The directed activities in this section provide a context in which to investigate the questions

· What is the relationship between area and perimeter in triangles? 

· What information is needed to determine the area of a triangle?

Focus	Investigate the relationship between area and perimeter in a triangle.
Technologies	Geometers Sketchpad and model 2_MaxTriangle.gsp
Background	The distance around a polygon is called its perimeter.  It is a sum of the length of the line segments or sides of the polygon. This should not be confused with the area of the polygon, which is a measure of the space enclosed by the sides of the polygon.  Figure 2.1 shows The Geometers Sketchpad model 2_MaxTriangle.gsp of a triangle.  Note that the area is given in terms of square centimeters, while the perimeter is given in terms of centimeters.   The perimeter may be changed by dragging point A’; and the relative lengths of the sides may be changed by dragging points B and C.  Figure 2.1:  Perimeter vs. Area
Tasks	Experiment with this model and answer the question, For any given perimeter, what shape triangle has the greatest area?