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A pyramid is a three-dimensional shape with one polygon base that is flat; and triangular sides that meet at a single point called the apex. Pyramids are named on the basis of the shape of their base. Like, a pyramid with a triangular-shaped base is called a triangular pyramid, and one that has a surface that is primarily square in shape is known as a square pyramid.

The following are the properties of a pyramid:

- It is a three-dimensional object, and has three dimensions, length, width, and height.
- It has a polygonal base, with sides that are triangular. The points of the triangles meet at a single point which is the apex.
- A pyramid has a defined number of edges and vertices (corners), depending on its base shape. As an example, a triangular pyramid has 6 edges and 4 vertices.
- All sides of a pyramid are triangular, and they all are of the same size and identical to one another.

Pyramids make an important application in geometry and have other real-world uses. It is often used to develop buildings and 3D models. Pyramids are also very significant in many other areas and are frequently seen in various fields of mathematics, engineering, and physics.

The amount of space occupied by the pyramid is the volume of a pyramid. The shape of the base of the pyramid determines the formula for the volume of a pyramid.

The formula for the volume of a pyramid with a rectangular base is:

V = (1/3)Bh

where V is the volume of the pyramid, B indicates the area of the base of the pyramid, and h is the pyramid height (the distance from the base to the apex).

The formula for the volume of a pyramid with a triangular base is:

V = (1/3)Bh

where V is the volume of the pyramid, B is the area of the pyramid base, and h is the pyramid height (the distance from the base to the apex).

The formula for the volume of a pyramid with a circular base is:

V = (1/3)πr^2h

where V is the pyramid volume, π is the mathematical constant almost equal to 3.14159, r is the radius of the pyramid base, and h is the pyramid height (the distance from the base to the apex).

For example:

Let us say, if a rectangular pyramid has a base 5 by 10 and a height 15, the volume of this pyramid will be:

V = (1/3)Bh = (1/3)(5*10)(15) = 250 cubic units

So the pyramid volume is 250 cubic units.

Note: The volume of a pyramid is always measured in cubic units. This is because it covers a three-dimensional space, contrary to other geometric figures that contain only two dimensions.