1
$\begingroup$

I've tried multiple variations of polygons but can't find any that work. Do they exist?

Is it possible to draw a polygon on a grid paper and divide it into two equal parts by a cut of the shape shown on the Figure (a)?

Solve the same problem for a cut shown on Figure (b).

Solve the same problem for a cut shown on Figure (c).

enter image description here

(In every problem a cut is inside the polygon, with the ends lying on the boundary. The sides of the polygons and the cuts must lie on the grid lines. The small links of the cuts are twice as short as the large ones)

$\endgroup$
  • $\begingroup$ Equal as in area? Or do they have to be the same shape? Also, can a cut be along one of the edges of the polygon? $\endgroup$ – Andrei May 11 '17 at 14:20
  • $\begingroup$ Just for the fun of it, is this a homework problem or one from the puzzle books? $\endgroup$ – Parcly Taxel May 11 '17 at 14:25
2
$\begingroup$

Here are (a) and (b). The key thing is to repeat the shape of the cut twice in the outline of the polygon.

enter image description here

EDIT: to add a solution for (c) constructed in a similar fashion.

enter image description here

$\endgroup$
0
$\begingroup$

enter image description here

So your polygon can be a rectangle?

You need $a^2=(a+b)(a+c)-a^2$

$a^2=a^2+ac+ab+bc-a^2$

$a^2=ac+ab+bc$

$\endgroup$
0
$\begingroup$

Here is something for (a) and (b)

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.