How is this possible? xD It has been bugging me for a long time!
(There is an image I ope it shows up)
I think I got it.
The red triangle has a base length of 8 squares and a height of 3. The green triangle has a length of 5 squares and is set 3 squares up from the bottom. That makes the space with the other two objects have an area of 15 squares (length x width L is the base of the green;5, and W is the height of the red;3, and so 5x3=15). When you switch the triangles, you are changing that space from 15 squares to 16 squares. The length becomes 8 (base of the red triangle) and the width becomes 2 (height of the green triangle), so the area left to fill is 16 squares.
Obviously, you can't take two pieces that fit together and have an area of 15 and move them to cover an area of 16.
The two large "triangles" are not actually triangles. If you hold a ruler up to the diagonals, they're not straight. The hypotenues' from the red and green triangles meet at a very wide angle (which only looks straight to our eyes). The smallest angle on the green triangle is 21.80' and on the red triangle it's 20.56'. Over the whole shape, this difference adds up to one whole square "missing" from the bottom shape.
If you look both shapes are made of the same 4 smaller shapes, with the same area, same height and length! The missing space should not be there as far as I know!
u just rearrange the shapes I cudnt see the print so I just looked at the shapes lol