What are the properties of pyramids? Types of pyramids and their shapes. Information on pyramids.
Properties Of Pyramids
The base of a pyramid is a polygonal region whose vertices are joined by line segments to a point not in the plane of the base. These line segments are called the lateral edges and the point where they meet is the apex of the pyramid. The side faces or lateral faces are triangular regions.
Like prisms we name pyramids according to the name of the polygon at the base.
The pyramids of Egypt are examples of square pyramids.
The line segment drawn from the apex perpendicular to the base is called the altitude of the pyramid, and its length is called the height of the pyramid. A right regular pyramid is a pyramid having a regular polygonal region as its base and having the centre of this region as one of the endpoints of the altitude, the other endpoint being the apex. The lateral faces of a right regular pyramid are all isosceles triangular regions. The length of the altitude of these isosceles triangular regions is called the siant height of the pyramid.
In the right square pyramid above:
the base is square region ABCD
the lateral faces are triangular regions SAB, SBC, SCD and SDA
the apex is point S
the lateral edges or slant edges are [SA], [SB], [SC] and [SD]
the height is |SO| or h the slant height is |SP| or s
The diagram on the left shows the net of our right square pyramid.
Yoıı can see that a square pyramid has 5 faces (4 triangular and 1 square), 8 edges (4 lateral and 4 on the base), and 5 vertices (4 on the base and 1 apex). Notice that :
So Euler’s formula is true for a square pyramid.