What is the area of a regular octagon, each of whose sides is $a$?
An octagon can be divided into a square, 4 rectangles, and 4 isosceles triangles.

![](https://cdn.mathpix.com/cropped/2024_05_02_41c15f5807302721362eg-1.jpg?height=344&width=341&top_left_y=197&top_left_x=881)

The area of the square is \(a^{2}\); the area of one rectangle is \(a \cdot a \sqrt{\frac{1}{2}}\); the area of one triangle is \(\frac{a^{2}}{4}\). Therefore, the area of the octagon is:

$$
a^{2} + 4 a^{2} \sqrt{\frac{1}{2}} + a^{2} = a^{2}(2 + 2 \sqrt{2}) = 2 a^{2}(1 + \sqrt{2})
$$

(Zoltán Harsányi, 6th grade, Eger.)

Number of solutions: 31.