Points E, F, G, H are proportion p along line segments AB, BC, CD, DE respectively.
How does the ratio of the shaded parallelogram to the area of ABCD depend on p?

To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.

A generalization of the Pythagorean Theorem, known to the ancients.
The purple parallelogram is the same area as the two blue ones combined.
Can you see why Pythagoras is a special case of this theorem?