I’ve looked at it. I’ve added it up. Hell, I even drew it, cut it out and tried to figure it out. But I’m too dumb.
Where the hell does the space come from?
Please help me because I can’t sleep until someone tells me how obvious the answer is and how dumb I am. 
(and if this is one of those “what rhymes with purple?” type questions which people try pulling please smack me now)
The top figure is not a perfect triangle, the diagonal bends very slightly inward. It’s hard to tell on a computer monitor, and the thickness of the lines probably disguises it even more. If you make another piece that represents the full triangle, 13 by 5 units, and draw the diagonal very precisely, then lay your existing pieces on it, you should see a thin sliver that’s missing. When you rearrange the pieces for the bottom figure, and switch the blue and red triangles, the triangle bends slightly outward, just enough for one square unit.
If you prefer a math approach, the area for the full triangle (13 by 5) should be 32.5 square units. Total up all of the pieces and it’s only 32 square units. You can also find that the slopes of the blue and red triangles aren’t the same.
That is the most annoying thing in the world. Do you know how long I spent dealing with that? I added up the area a million times, and thought that I was just missing something! (well, apparently I was!)
I wasn’t kidding when I said I made cutouts.
All that for a stupid optical illusion/trick.
“oh I could while away the hours, conferrin’ with the flowers
Consultin’ with the rain.
And my head I’d be scratchin’ while
my thoughts were busy hatchin’
If I only had a…:smack:”
Agreed. Look carefully at how the outline of the triangles meet the lines of the grid as I’ve circled them here and you can compare them a little easier. Look soon because I’m not keeping the image up for two terribly long lest it be a puzzle spoiler for everyone.
