[b]Introduction and Background[/b][br] [br]The area of a triangle, like other polygons, is determined by finding out how many unit[br]squares it takes to cover the triangle.  But, as you saw in an earlier [i]GeoGebra [/i]lab, unit squares don’t nicely cover a polygon like a triangle.  [br] [br]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:[br][b]Area of rectangle = base X height[/b][br] [br]For this activity, you are going to generate six different triangles and have [i]GeoGebra[/i] compute their area in unit squares.  Then you will try to find a pattern in your data.[br] [br][b]Step 1.   [/b][b] GeneratingData on Triangles and their Area[/b][br][b] [/b][br] Use the MOVE tool [icon]/images/ggb/toolbar/mode_move.png[/icon] to drag the blue corner points of the triangle, changing it into[br]six triangles with [i]different[/i] heights and bases.  As you construct the triangles, fill in a Data Table row for each triangle you create.[br][br][table] [tr] [td][i][b]Data Table[/b][/i] [/td] [/tr] [tr] [td][u][b]Triangle[/b] [/u][/td] [td][u][b]  Base in Units  [/b] [/u][/td] [td][u][b]  Height in Units  [/b] [/u][/td] [td][u][b]  Area in Unit Squares  [/b][/u] [/td] [/tr] [tr] [td][b]Triangle 1[/b][br] [/td] [td][br] [/td] [td][br] [/td] [td][br] [/td] [/tr] [tr] [td][b]Triangle 2[/b][br] [/td] [td][br] [/td] [td][br] [/td] [td][br] [/td] [/tr] [tr] [td][b]Triangle 3[/b][br] [/td] [td][br] [/td] [td][br] [/td] [td][br] [/td] [/tr] [tr] [td][b]Triangle 4[/b][br] [/td] [td][br] [/td] [td][br] [/td] [td][br] [/td] [/tr] [tr] [td][b]Triangle 5[/b][br] [/td] [td][br] [/td] [td][br] [/td] [td][br] [/td] [/tr] [tr] [td][b]Triangle 6[/b][br] [/td] [td][br] [/td] [td][br] [/td] [td][br] [/td] [/tr][/table][b] [/b][br][b]Step 2.   [/b][b]Search for a Pattern[/b][br][b] [/b][br]Look for a pattern in the data. [br] [br]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. [br] [br] Describe your method and write a formula: