Geometry is Easy?
It is, indeed
Consider the green triangle. The base is 5 units and height is 2 units. tan x = 2/5. The red triangle has 8 units base and 3 units height hence tan y = 3/8. Since the bases are parallel, and the angles are not equal, The given figure is not a triangle :). It is only our illusion that we take it to be a triangle.
Probably, Raghu will draw another wonderful figure taking these into coniderations and give us a better 'picture'
Yeah, thats right. I used the same reasoning - using slopes - to intially prove it for myself. But I found that I couldn't completely satisfy my friends with that explanation.
And YOU,....made me draw THIS: (refer to the attached image)
and Here goes my explanation:
You IMAGINE a triangle, shown by the thin black outline (hypotenuse).
On the other hand, ONLY the coloured parts P1, P2, P3 and P4 are present.
...which do not quite make up a triangle.
There is already a hole in the first picture - the difference between what you THINK the figure is, and what it REALLY IS.
(You may need to Zoom-in on the picture a bit to notice the white gap between the hypotenuse of YOUR triangle and the coloured parts.)
Now, in the second arrangement, the coloured parts overshoot the border thus giving space for a larger hole.
(See the coloured blocks extending beyond the hypotenuse?)
So to answer the question "Where does the hole come from?" in simpler terms, I would say ...
"You started with a distorted triangle with hypotenuse bent slightly inwards, and then distortded it again so that the hypotenuse is now slightly bent outwards. The area THUS gained is what accommodates the hole."