This movie shows the values of w and the area of the P-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-P worksheet to show it frame-by-frame).

Just as with the T-shape, 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 P-shape on squared paper, using a multiple of 2 units, rather than a length of 1, for the sides of the bounding square. This again results in friendlier numbers.

It can be illuminating to compare the area of the square 'leg' with the adjacent 'white gap' (ie the rectangle that has been removed from the unit square to form the P-shape). We do this more explicity on the next page.