This movie displays the values of w and the area of the T-shape, as w changes.
Can you spot when the area is a mimimum? You might want to PAUSE the movie at various points, since the numbers change so rapidly (or use the arrow keys or the JAVA-T worksheet to show it frame-by-frame).

The range of values taken by the area is larger than for the M- and N-shapes but still fairly small, and we have again measured the area to several (4) decimal places. The minimum area (of 0.75) is fairly easy to spot this time: it occurs when w = 0.5, so the question, "Roughly what fraction (of 1) is this?", is much more obvious than for the M- and N-shapes.

It might be worth drawing examples of the T-shape on squared paper, using a multiple of 4 units, rather than a length of 1, for the sides of the bounding square. This again results in friendlier numbers.

On the next two pages we go through the same procedure with the P-shape. This is very similar to the T-shape, except that the 'leg' has been moved to the left hand side, so that the two 'white' sections now form a single region. This makes the task easier to analyse, as we shall see.