Polygons on a grid

Question

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).

(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)

Answer 1

So your polygon can be a rectangle?

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

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

$a^2=ac+ab+bc$

Answer 2

Here is something for (a) and (b)

Answer 3

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

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