GeoGebra 4.0: Area of a Trapezoid Activity: Area of a Trapezoid Objectives 1. Becoming familiar with advance features and motion in GeoGebra 2. To understand the formula for the area of a Trapezoid and how this translates to a construction in GeoGebra. •
Introduction: In this activity you are going to use the following tools. Make sure you know how to use each tool before you begin with the actual construction: Move Slider Perpendicular line Intersect two objects New point Segment between two points Line through two points Polygon Rotate object around point Midpoint or center by angle Hint: You might want to have a look at the file, Trapezoid_Area.ggb, if you are not sure about the construction process. Preparing the Window: • Open a new GeoGebra file. • Hide the algebra window and the axes. Set labeling to New Points Only. Construction process: 1. Use the line through two points tool and create line a. 2. Use the new point tool and create point C not on line a. 3. Use the perpendicular line tool and create line b through point C and perpendicular to line a. 4. Use the perpendicular line tool and create line c through point C and perpendicular to line b. 5. Use the new point tool and create point D on line c. 6. Use the intersects two objects tool to create intersection point E between lines a and b. 7. Use the polygon tool to create polygon ABDC. 8. Use the segment between two points tool and create segment d from point A to point E. Hint: Make this a dashed segment. 9. Use the segment between two points tool and create segment e from point C to point E. Hint: Make this a dashed segment, change its name to h and show the label as name. 10. Use the slider tool and click any where on the screen to create angle α *Select the option for number slider leave the name α and Min: 00 Max: 1800. 11. Use the midpoint tool and create the midpoint F between points D and B. GeoGebra 4.0: Area of a Trapezoid 12. Use the rotate object around point by angle tool and select the polygon ABCD, point F, use angle α and select clockwise. Hint: This creates a new trapezoid. The following Image is what your file should look like before hiding any objects or formatting the polygons. Formatting: Select Edit Object properties and format your object in anyway you wish and save your file. Challenge Questions: 1) How does this file assist you in proving why the area formula for a Trapezoid !
is ! = ! !! + !! ℎ?