Octahedron volume

From ancient times, people needed to measure the amount of various substances. Bulk substances and liquids could be measured by filling them with vessels of a certain capacity, determining their quantity by volume. The concept of volume in solid geometry is introduced similarly to the concept of area in plane geometry. In plane geometry, we determined the area like this: the area of ​​a polygon is the value of the part of the plane that the polygon occupies. To formulate the concept of volume similarly to this concept. The magnitude of the part of the space occupied by the geometric body is called the volume of this body. Volume is measured in "cubic" units.

Octahedron — is one of the five convex regular polyhedra - Platonic solids. The octahedron has eight triangular faces, twelve edges, six vertices, four sides converge to each of its vertices.

The octahedron can be divided into two equal pyramids. Where the volume of one pyramid is equal to (base area × height) / 3. Therefore, the volume of the octahedron = 2 × the volume of the pyramid. In the case of the right octahedron, the base area equal a².