Truncated pyramid 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.

A truncated pyramid is a polyhedron whose vertices are the vertices of the base and the vertices of its section with a plane parallel to the base. Properties of a truncated pyramid: Lateral faces of a truncated pyramid - a trapezoid. The lateral ribs of a regular truncated pyramid are equal and equally inclined to the base of the pyramid.

The volume of the truncated pyramid(or frustum of a pyramid) is equal to one third of the product of height h by the sum of the areas of the upper base S₂, the lower base of the truncated pyramid S₁ and the average proportional between them.