## Task 1 - 260611

A square $A B C D$ with a side length of $8 \mathrm{~cm}$ has a square $E F G H$ with a side length of $2 \mathrm{~cm}$ inscribed in it, as shown in the image. $H G$ and $D C$ are parallel segments with a distance of $2 \mathrm{~cm}$ between them. $E H$ and $A D$ are parallel segments with a distance of $2 \mathrm{~cm}$ between them.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0254.jpg?height=326&width=282&top_left_y=454&top_left_x=1458)

a) Calculate the area of the shaded region in the image!

b) The shaded area is to be divided into five parts. These parts should be designed in such a way that any two of them can be brought into coincidence by rotating or translating them.

Draw such a division of the shaded area!

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0254.jpg?height=260&width=257&top_left_y=984&top_left_x=314)
a) The squares $A B C D$ and $E F G H$ have areas of $64 \mathrm{~cm}^{2}$ and $4 \mathrm{~cm}^{2}$, respectively, because $8 \cdot 8=64$ and $2 \cdot 2=4$. Therefore, the shaded area has an area of $60 \mathrm{~cm}^{2}$ because $64-4=60$.

b) The diagram shows one possible solution to the problem.