Parrallelcircuits is on the right track.
The two triangles have the same area, they are just arranged differently, and the drawing is not an honest one, or you would see it right away.
If you look closely at the original post of the two triangles, the top line of the lower triangle actually rises at a slightly higher angle than the top triangle'* top line.
To see this, just follow the two top lines as they rise to the right, and compare where the top line is in relation to the boxes as the top line rises on each of them. The lower triangle'* top line rises faster.
So it'* a slightly different angle, but on the bottom triangle, the drawing cheats by slightly bending the line a little as it gets to the top so it hits the box at the same place the upper triangle does.
In real life, the bottom triangle is really slightly taller. The drawing cheated.
If you took some paper and cut out these pieces and arranged them like the drawing, I would bet that your bottom triangle would be slightly taller than the top one.
So the slightly taller triangle'* area is arranged differently, enough to equal an empty box on the grid.
But this drawing cheats to make it look like they are the same size.
It'* an illusion.
Something that might help to understand is a door on your house that doesn't seal properly. That small gap between the door and the jamb might be really small, but if it was all scrunched down into a square hole, you could probably get your fist through it. A lot of air can get through it, and you can hardly see the gap.
1996 Olds LS, 198,900 miles: RIP...