its because they dont fit perfectly in each other, so the rectangle cant really exist, just take the slopes of the hypotenuse on the triangles as the slopes of the long side of the trapezoids, the triangles have a slope of 8/3 (2.33) and the traezoids have a slope of 5/2 (2.5) , it only looks like they line up
It's a simple matter of changing the area. Think of it in simpler term: a 2x2 block. It has a perimeter of 8 and an area of 4. If you change the perimeter to be 1x3, it would keep the perimeter of 8 but the new area would only be three. The only reason the animation throws you off is because it starts with a designated number of squares and seems to add one out of nowhere.
no it isn't... the hypotenuse is not straight on the triangle, this tiny bow in the line which is practically imperceptible to the eye over the 13 squares loses a square. so yeah...
The slopes of the trapezoids and triangles do not match
the slope of the trapezoids have a Rise/Run of 2/5
the triangles have a rise/run of 3/8
2/5= 0.4
3/8=0.375
this means that there is a tiny gap between shapes, resulting in about 1 unit
Area lost = AreaOrange - AreaRed = 0.3125cm^2
Area lost * 2 = totalAreaLost = 0.625cm^2
Or in simpler terms, the slopes simply don't match up and the creator of the GIF made them look like they were. Not sure if I calculated it right or all of it, but I can't be bothered spending more than 5 minutes on one piece of content, so I don't really care. :D