In GeoGebra the value of a polygon in the Algebra View corrisponds with its area. We can use this in an exercise in which one has to drag the vertexes to form a rectangle with given area. You can form a polygon out of free points, but in this case we define the vertexes of it so that the polygon always remains a rectangle.

In next applet you have to drag two points to give the rectangle a given area. See how the applet works and make it yourself following the construction steps.

[table][tr][td]1[/td][td][/td][td]Type the command [b]listsol=Shuffle[4, 6, 8, 10, 12, 16, 18, 20, 24][/b] to define listsol.[/td][/tr][tr][td]2[/td][td][/td][td]Type the command [b]sol=listsol(1)[/b] to define the number sol.[/td][/tr][tr][td]3[/td][td][icon]/images/ggb/toolbar/mode_point.png[/icon][/td][td]Select the Point Tool and click on the origin to create the point A.[br]Alternatively you can type the command [b]A = (0, 0)[/b].[/td][/tr][tr][td]4[/td][td][icon]/images/ggb/toolbar/mode_point.png[/icon][/td][td]Select the Point Tool and click on the x-Axis to on the positive side to create a point.[br]Rename the point to AA.[/td][/tr][tr][td]5[/td][td][icon]/images/ggb/toolbar/mode_ray.png[/icon][/td][td]Select the Ray Tool and click on A and AA to create a ray f.[/td][/tr][tr][td]6[/td][td][icon]/images/ggb/toolbar/mode_point.png[/icon][/td][td]Select the Point Tool and click on the ray to create a point B.[br]Drag this point to the position (1, 0).[/td][/tr][tr][td]7[/td][td][/td][td]Type the command [b]D = Point[Ray[A, (0,3)]][/b] to define the point D.[br]This one command has a similar result as the previous three steps: it creates a point on a ray but with the advantage that no auxiliary objects have to be hidden afterwards.[br]Drag D to the position (0, 1). [/td][/tr][tr][td]8[/td][td][/td][td]Type the command [b]C = (x(B), y(D))[/b] to create a point C.[/td][/tr][tr][td]9[/td][td][icon]/images/ggb/toolbar/mode_polygon.png[/icon][/td][td]Select the Polygon Tool and click successively on the points A, B, C, D and again on A to create the rectangle poly1.[br]Alternatively you can define the polygon by the command [b]Polygon[A, B, C, D][/b].[br]Rightclick on it to define its dynamic colors (see below).[/td][/tr][tr][td]10[/td][td][icon]/images/ggb/toolbar/mode_text.png[/icon][/td][td]Select the Text Tool and type the dynamic text of the exercise.[br]Select poly1 in the list of available objects.[/td][/tr][tr][td]11[/td][td][icon]/images/ggb/toolbar/mode_buttonaction.png[/icon][/td][td]Select the button Tool and create a button wich caption [b]next exercise[/b] and scripting commands[br][b]UpdateConstruction[][br]SetValue[B,(1,0)][br]SetValue[D,(0,1)][/b][br][/td][/tr][/table]