The concept of the pyramid

The concept of the pyramid

The pyramid is a geometrical shape with many surfaces, one of its sides is a polygon called the base of the pyramid, and it is produced by linking the corners of its base to a point that does not lie at the level of the base itself and is called the top of the pyramid. The straight lines at which each side meets two sides are called letters or side edges, while the polygons from which the pyramid is built are called faces, and each pyramid can be named according to the shape of its base. And when not The base of the pyramid is specific, often a square pyramid with a square base.

Types of pyramids

Regular pyramid

• Its base is a regular polygon.
• The location of the pillar falling from the top of the pyramid at the base of it represents the center of the pyramid.
• Its sides are identical and are of equal legs.
• Its side edges are equal in length.
• The height of the side pyramid is uniform in length.
• The height of the regular pyramid is the height of the falling column from the top of the pyramid to the geometric center of the base, where the geometric center is the center of the circle that touches the ribs of the polygon from the inside or passes through its heads.

Pyramid with regular faces

It is any form of pyramids, which consists of regular side faces, just as the triangular pyramid whose base and side faces are equilateral triangles becomes irregular and tetrahedron shape.

The star pyramid

Its base is a regular stellar polygon. For example, a pyramid whose base is a five-pointed star and which has five triangular sides is called an astral pyramid.

The missing pyramid

• When a pyramid is cut at a plane parallel to the base, the remaining part of the pyramid (the part enclosed between the segment and the base) is called an incomplete pyramid.

Notes:

• The number of sides of the base of the pyramid is equal to the number of side faces in it.
• The number of heads of the base of the pyramid is equal to the number of side edges of it.

The area and size of any pyramid

The area of ​​the side faces of the existing pyramid is equal to half the circumference of the base times the height of the side face as follows:

• Area of ​​facets of the existing pyramid: 12 x base circumference x lateral height.
• Pyramid size: One third of the base area (calculated according to the geometrical shape of the base using the laws of the area) times the height of the pyramid, i.e.: the pyramid size = 13 x the base area x height.

The area and size of the missing pyramid

Since the missing pyramid has two bases, the area of ​​its side faces is equal to half of the total circumference of the two bases multiplied by the height of the side face as follows:

• Area of ​​side faces of the existing pyramid: 12 x sum of the circumference of the two bases x lateral height.
• Size of the pyramid: Using the area of ​​the two bases and the height, the law is: the size of the missing pyramid = 13 x the height of the pyramid x (the area of ​​the first base + the area of ​​the second base + the square root of the product of multiplying the area of ​​the two bases).