The triangle question: IF you look at the first image, the slope of the main triangle is not actually a straight line, though very close to one. Because the slope of the two smaller triangles are not the same. You can tell by the ratio of their perpendicular and base sides - 2:5 and 3:8. The slope of the red triangle (with sides 3 and 8 units) is slightly less than the smaller one (with sides 2 and 5). So in the first image, the straight line is actually bending inwards, taking up the space of that single square you see in the 2nd picture. In the 2nd picture, when the smaller triangles are switched, the line is bending outwards, freeing up space for that single square unit.