Hello, decadyne!

This is a classic "paradox" . . . quite baffling until explained.

The small right triangle has legs 2 and 5.

The smaller acute angle is: $\displaystyle \arctan(0.4) \approx 21.8^o$

The large right triangle has legs 3 and 8.

The smaller acute angle is: $\displaystyle \arctan(0.375) \approx 20.6^o$

The two triangles are __not__ similiar and hence are not interchangeable.

Code:

* B
* |
* 21.8° | 2
* - - - - - *
* | 5
* | 3
* 20.6° |
A * - - - - - - - - - - - *
8

Although the diagonal AB is supposed to be a straight line,

. . but there is an imperceptible "dip" in the middle.

There is a very narrow triangular strip missing.

. . And that triangle has an area of a half square unit.

If the two right triangles are switched, the diagonal "bulges" in the middle.

. . The extra area is a half square unit.