A $3 \mathrm{~m}$ side square-based newspaper pavilion's roof structure consists of two intersecting regular triangular prisms, one of whose side faces coincides with the ceiling. (The two prisms are rotated $90^{\circ}$ relative to each other.) What is the size of the roof area?
Solution. The diagram shows the structure of the roof truss that matches the description. Except for the edges marked with dashed lines, every edge of the body is 3 meters long.

![](https://cdn.mathpix.com/cropped/2024_05_02_8cecda1e76af1c2f0345g-1.jpg?height=483&width=501&top_left_y=260&top_left_x=801)

The roof truss consists of two types of plane figures. One is a regular triangle (for example, the triangle $A B C$), with each side being 3 meters. The total area of the four regular triangles is:

$$
4 \cdot \frac{3 \cdot \frac{3 \sqrt{3}}{2}}{2}=9 \sqrt{3}
$$

The other type of plane figure appears eight times, such as the triangle $C B D$. The area of this triangle is one-fourth of the area of the square side of the prism, which is $\frac{3 \cdot 3}{4}$. The total area of the eight such triangles is:

$$
8 \cdot \frac{3 \cdot 3}{4}=18
$$

The area of the roof surface is $18+9 \sqrt{3}$ square meters if we include the four triangular faces, and 18 square meters if we do not include them.