A number of DPWW are based on the additivity property of areas. In these proofs, a region is cut up into parts, which are then rearranged to form a better known shape. Even though these proofs can be very elegant, without proper justification of the constructions they can be misleading. A famous example of this is the "Missing Square" paradox.

[b]Example 3. The Area of the Regular Dodecagon[/b][br]This example is based on the well-known Kürschák’s tile. The dynamic rearrangement of the tiles makes a convincing case that the area of the dodecagon is ¾ of the area of the circumscribed square, but this proof should be supplemented by a few lines of calculations showing that certain triangles are congruent.[br][br][url=https://tube.geogebra.org/m/1352433][size=85]More details.[/size][/url]

[b]Example 4. The midsegments divide any triangle in four congruent triangles.[/b][br]Other DPWW are completely self-explanatory and do not need any additional calculations.[br]One such construction can be seen in the example below. Here the proof is based on properties of the medians and the fact that rotations preserve the area.[br][br][url=https://tube.geogebra.org/m/82097][size=85]More details.[/size][/url]