The first paragraph of the book is devoted to the proof of the following theorem, found by mathematicians Boya and Gerwin: if two polygons have the same area, then one of them can be divided into such parts that it is possible to make a second polygon. Shorter formulation: if two polygons are equal, they are equal. The study of some issues related to the equivalence of figures is devoted to the whole book as a whole . It is divided into two chapters, in the first of which polygons are studied, and in the second - polyhedrons.. The above theorem is one of the main in the first chapter. In the second chapter, Dan's theorem is most interesting: there are polyhedra that have the same volume (equals), but are not equal. The Boi-Gerwin and Dan theorems are proved in paragraphs 1 and 5., respectively. Paragraphs 2-4, 6 give the results of the most recent years (at the time of the book's release) which belong to Hadwiger, Glr, Sidler. The simplest in the book are the three to four first paragraphs. To understand them requires knowledge of about eight years of high school. The next most difficult part of the book is the fifth paragraph and the beginning of the sixth . They require knowledge of almost the entire school course of geometry and the ability to think well. Finally, the rest, the most difficult part of the book (small print) is designed mainly for students of pedestals and universities. Other issues of the series: . 01. - Markushevich A . and . Return sequences. Issue. 02. - Nathanson and . P. The simplest tasks to the maximum and minimum. Issue. 03. - Sominsky I. C. Method of mathematical induction. Issue. 04. - Markushevich A . and . Wonderful Curves. Issue. 05. - Korovkin P. P. Inequality. Issue. 06. - Vorobyov N . N. Fibonacci Numbers. Issue. 07. - Kurosh A. G. Algebraic equations of arbitrary degrees. Issue. 08. - Gelfond A. About. Solving equations in integers. Issue. 09. - Markushevich A . and . Areas and logarithms. Issue. 10. - Smogorzhevsky A. C. Coordinate Method. Issue. 20. - Lopshitz A. M. Calculation of the area of oriented figures. Issue. 21. - Head L. and . , Yaglom I. M. Induction in Geometry