TASK

This is a relatively straightforward task that benefits from having lots of solutions. If students balk at the term 'shear' you could loosen the wording to "Find ways of dragging one vertex of the triangle that help to show ...".
[Of course, such dragging might not produce a shear, and so might not preserve area.]

It is easy to find the area of the triangle without transforming it: in this diagram (right) the surrounding rectangle has an area of 18 unit squares, and the outer triangles have an area of 1.5 + 4.5 + 6 = 12, so ABC has an area of 18 – 12 = 6.
However, our interest is not in evaluating the area but in finding shears that make the value more 'visible' (anschaulich...).

In these files we see what happens when C is moved, or A is moved, or B is moved. Our focus is on transforming the triangle in such a way that it is easy to construe the size of the base and the height.

We also provide a JAVA worksheet that allows the user to drag points A, B and C freely - and to read-off (or hide) the area of the resulting triangle. You might want to use this after seeing the first few movies.

On the next page we show some salient positions for C.

FREE:
a high-res pdf file of this new GEOaa-zz task