Find the volume of a regular hexagonal prism with each edge equal to 2.

In order to solve the problem, recall the formula for finding the volume of a prism:

Prism volume – base area multiplied by height:

V = S main * h.

The base area consists of 6 regular triangles:

Sb = 6 * S treug.

Let’s find the area of one regular triangle:

S triang = 1/2 * a * b * sin (α), where a and b are the sides of the triangle, sin (α) is the angle between them.

S triug = 1/2 * 2 * 2 * sin60 = 1/2 * 2 * 2 * √3 / 2 = √3 sq. units

Sb = 6 * √3 = 6√3.

V = 6√3 * 2.

V = 12√3 cubic meters units

Answer: V = 12√3 cubic meters. units