Pointless note: Another way to solve that triangle is to flip the left-most leg of it counterclockwise until it's exactly parallel with the rectangle. It is then plain to see it's half of the rectangle.
Do you mean rotate the triangle counter-clockwise? The leftmost leg of the triangle is longer than the left edge of the rectangle, so I don't think it will be as plain as you suggest. You'll end up with something like this: