Discover the formula for the Area of a Triangle
Instructions
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 triangle. But, as you saw in an earlier GeoGebra lab, unit squares don’t nicely cover a polygon like a triangle.
You also learned that the area of a triangle can be related to the area of a rectangle, so perhaps a formula for the area of a triangle is related to the formula for the area of a rectangle:
Area of rectangle = base X height
For this activity, you are going to generate six different triangles and have GeoGebra compute their area in unit squares. Then you will try to find a pattern in your data.
Step 1. GeneratingData on Triangles and their Area
Use the MOVE tool 
to drag the blue corner points of the triangle, changing it into
six triangles with different heights and bases. As you construct the triangles, fill in a Data Table row for each triangle you create.
| Data Table |
| Triangle | Base in Units | Height in Units | Area in Unit Squares |
| Triangle 1
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| Triangle 2
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| Triangle 3
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| Triangle 4
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| Triangle 5
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| Triangle 6
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Step 2. Search for a Pattern
Look for a pattern in the data.
If you know a triangle’s base and height, do you see a way to compute the area of a triangle without counting unit squares on a grid? Remember, the formula for the area of a triangle appears to be related to the formula for a rectangle.
Describe your method and write a formula: