Find the volume of a regular hexagonal prism with all edges equal to √3.

The base of the prism is a regular hexagon, which can be divided into 6 regular triangles, all sides of which are equal to √3. The area of one triangle can be found using Heron’s formula.

The semi-perimeter of such a triangle:

p = (3√3) / 2;

Str = √ ((3√3) / 2 * (3√3 / 2 – √3) ^ 3) = √ ((3√3) / 2 * (√3 / 2) ^ 3) = (√3 / 2) ^ 2 * √3 = (3√3) / 4.

Base area:

Sb = 6 * Str = 6 * (3√3) / 4 = (9√3) / 2.

Prism volume:

V = S main * h = (9√3) / 2 * √3 = (9 * 3) / 2 = 13.5.

Answer: 13.5.