Rectangle with given area

always a rectangle

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.

Drag the points to match the given area

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.

Try it yourself...

Construction Steps

1Type the command listsol=Shuffle[4, 6, 8, 10, 12, 16, 18, 20, 24] to define listsol.
2Type the command sol=listsol(1) to define the number sol.
3Toolbar ImageSelect the Point Tool and click on the origin to create the point A. Alternatively you can type the command A = (0, 0).
4Toolbar ImageSelect the Point Tool and click on the x-Axis to on the positive side to create a point. Rename the point to AA.
5Toolbar ImageSelect the Ray Tool and click on A and AA to create a ray f.
6Toolbar ImageSelect the Point Tool and click on the ray to create a point B. Drag this point to the position (1, 0).
7Type the command D = Point[Ray[A, (0,3)]] to define the point D. 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. Drag D to the position (0, 1).
8Type the command C = (x(B), y(D)) to create a point C.
9Toolbar ImageSelect the Polygon Tool and click successively on the points A, B, C, D and again on A to create the rectangle poly1. Alternatively you can define the polygon by the command Polygon[A, B, C, D]. Rightclick on it to define its dynamic colors (see below).
10Toolbar ImageSelect the Text Tool and type the dynamic text of the exercise. Select poly1 in the list of available objects.
11Toolbar ImageSelect the button Tool and create a button wich caption next exercise and scripting commands UpdateConstruction[] SetValue[B,(1,0)] SetValue[D,(0,1)]