Can anyone tell me please where does the gap come from?
Thanks and sorry if the question is not exactly relevant, I just didn't know where else to ask.
Can anyone tell me please where does the gap come from?
Thanks and sorry if the question is not exactly relevant, I just didn't know where else to ask.
Figure out the area of the little gap in the middle:
(you can probably guess it, but it's easy to calculate).
Try it for yourself before peeking at the explanation at the bottom.
From there it's easy to see where the area for the square comes from.
Total area of the 13 × 5 region = 65 squares.
Total area of the two unmarked rectangular parts = (5 × 3) × 2 = 30
Total area of blue triangles = (5 × 2 × ½) × 2 = 10
Total area of red triangles = (8 × 3 × ½) × 2 = 24
Remaining area = 65 - 30 - 10 - 24 = 1 square.
If it's still not clear, rotate the upper two triangles each about the center of its own diagonal (which leaves the upper edge of the gap unchanged), you get the triangles from your two diagrams overlaid on each other in the correct positions:
It takes the extra square to make up for the area of that skinny parallelogram-shaped gap between the regions covered by the two arrangements of shapes.
The line over the red part is not quite as steep as that over the blue part. Just compute the two slopes and you'll see that.