Problems

Cut an arbitrary triangle into 3 parts and out of these pieces construct a rectangle.

Suppose that a rectangle can be divided into \(13\) equal smaller squares. What could be the side lengths of this rectangle?

Daniel has drawn on a sheet of paper a circle and a dot inside it. Show that he can cut a circle into two parts which can be used to make a circle in which the marked point would be the center.

Is it possible to cut such a hole in \(10\times 10 \,\,cm^2\) piece of paper, though which you can step?

Cut the following shape into four equal figures.

Cut the following shape into two equal parts.

Cut the "biscuit" into 16 congruent pieces. The sections are not necessarily rectilinear.

Is it possible to cut this figure, called "camel"

• a) along the grid lines;

• b) not necessarily along the grid lines;

into \(3\) parts, which you can use to build a square?
(We give you several copies to facilitate drawing)

Cut a \(7\times 7\) square into \(9\) rectangles, out of which you can construct any rectangle whose sidelengths are less than \(7\). Show how to construct the rectangles.

Cut a square into five triangles in such a way that the area of one of these triangles is equal to the sum of the area of other four triangles.