The base side of a regular hexagonal pyramid is 12 cm, its lateral edge forms an angle

The base side of a regular hexagonal pyramid is 12 cm, its lateral edge forms an angle of 45 with the base plane. Find the volume of the pyramid.

Since the base is a regular hexagon, its area is equal to the area of six equilateral triangles formed at the intersection of the diagonals.
Sb = 6 * Saov = 6 * AB2 * √2 / 4 = 6 * 144 * √2 / 4 = 216 * √2 cm2.
Consider a right-angled triangle AOM, in which the leg AO = 12 cm, and the angle MAO = 450.
Since in a right-angled triangle one of the angles is 450, the triangle is isosceles, and AO = MO = 12 cm.
Let’s define the volume of the pyramid.
V = Sbase * MO / 3 = 216 * √2 * 12/3 = 864 * √2 cm3.
Answer: The volume of the pyramid is 864 * √2 cm3.