In this publication, we will consider the definition, main elements, types and possible options for the section of the pyramid. The presented information is accompanied by visual drawings for better perception.
Pyramid Definition
Pyramid is a geometric figure in space; a polyhedron that consists of a base and side faces (with a common vertex), the number of which depends on the number of corners of the base.
Note: pyramid is a special case.
pyramid elements
For the picture above:
- Base (quadrangle ABCD) – a face of a figure that is a polyhedron. She does not own the top.
- The top of the pyramid (point E) is the common point of all side faces.
- Side faces are triangles that converge at a vertex. In our case, this is: General Conditions of Purchase, AED, BEC и CED.
- Side ribs – the sides of the side faces, with the exception of those that belong to the base. Those. this is AE, BE, CE и DE.
- Pyramid Height (EF or h) – a perpendicular dropped from the top of the pyramid to its base.
- Side face height (EM) – the height of the triangle, which is the side face of the figure. In a regular pyramid are called apothematic.
- Surface area of the pyramid is the area of the base and all its side faces. Formulas for finding (the correct figure), as well as pyramids, are presented in separate publications.
Pyramid development – the figure obtained by “cutting” the pyramid, i.e. when all its faces are aligned in the plane of one of them. For a regular quadrangular pyramid, the development in the plane of the base is as follows.
Note: presented in a separate publication.
Sectional views of the pyramid
1. Diagonal section – the cutting plane passes through the top of the figure and the diagonal of the base. A quadrangular pyramid has two such sections (one for each diagonal):
2. If the cutting plane is parallel to the base of the pyramid, it divides it into two figures: a similar pyramid (counting from the top) and a truncated pyramid (counting from the base). The section is a base-like polygon.
In this picture:
- pyramids EABCD и EA1B1C1D1 similar;
- quadrangles ABCD и A1B1C1D1 are also similar.
Note: There are other types of cut, but they are not so common.
Types of pyramids
- Regular pyramid – the base of the figure is a regular polygon, and its vertex is projected into the center of the base. It can be triangular, quadrangular (pictured below), pentagonal, hexagonal, etc.
- Pyramid with a side edge perpendicular to the base – one of the side edges of the figure is located at a right angle to the plane of the base. In this case, this edge is the height of the pyramid.
- Truncated pyramid – the part of the pyramid that remains between its base and a cutting plane parallel to this base.
- Tetrahedron – This is a triangular pyramid, the faces of which are 4 triangles, each of which can be taken as a base. Is correct (as in the figure below) – if all edges are equal, i.e. all faces are equilateral triangles.
