5.1. $[5-6.4$ (а. - 10 points, б. - 20 points)] On a grid paper, a figure is drawn (see the picture). It is required to cut it into several parts and assemble a square from them (parts can be rotated, but not flipped). Is it possible to do this under the condition that a) there are no more than four parts; b) there are no more than five parts, and all of them are triangles? If yes, show how to do it; if no, prove that it is impossible.

![](https://cdn.mathpix.com/cropped/2024_05_06_57731af2d159c5caf22cg-2.jpg?height=268&width=394&top_left_y=2313&top_left_x=1531)
Answer: a) yes; b) yes.

Solution. Possible cutting options for parts a) and b) are shown in Fig. 5, a) and b).

![](https://cdn.mathpix.com/cropped/2024_05_06_57731af2d159c5caf22cg-3.jpg?height=254&width=368&top_left_y=204&top_left_x=227)

Fig. 5, a)

![](https://cdn.mathpix.com/cropped/2024_05_06_57731af2d159c5caf22cg-3.jpg?height=300&width=308&top_left_y=158&top_left_x=614)

![](https://cdn.mathpix.com/cropped/2024_05_06_57731af2d159c5caf22cg-3.jpg?height=254&width=368&top_left_y=204&top_left_x=1141)

![](https://cdn.mathpix.com/cropped/2024_05_06_57731af2d159c5caf22cg-3.jpg?height=305&width=323&top_left_y=153&top_left_x=1523)

Fig. 5, b)