How many four-sided figures can be traced in a rectangle that has a letter A inside it (arms from the middle of the top edge to the bottom corners) and a flat line across its middle?

Rectangles: the top strip, the bottom strip and the whole, 3. With part of the top edge as a side: on each side of the A, the piece above the flat line, that piece reaching past the far arm, and the piece down to the base, $3+3=6$. With the flat line as the top side: 3 trapeziums below it. Total $3+6+3=12$.