COMPUTING THE AREA OF TRIANGLES
Introduction and Background
The area of a triangle, like other polygons, is determined by finding out how many unit squares it takes to cover the shape.
But what if we don’t want to simply sit and count using a grid or by moving a unit square around on a rectangle? Is there another way?
For this activity, you are going to construct different triangles and have GeoGebra compute their area in unit squares.
Then you will try to find a pattern in your data.
Step 1. Construct Differing Triangles
Use the MOVE (pointer) tool to drag the corner points of each triangle, changing them into six triangles with different heights and bases. As you construct the triangles, fill in the Data Table for each triangle you create.
Data Table
Triangle............Base in Units............Height in Units............Area in Unit Squares
Triangle 1
Triangle 2
Triangle 3
Triangle 4
Triangle 5
Triangle 6
Step 2. Search for a Pattern
Look for a pattern in the areas. Do you see a way to use arithmetic to compute the area of a triangle without counting unit squares? Describe your method: