Solid Geometry
     Pyramids
      Regular square pyramid
      Regular triangular pyramid
      Regular hexagonal pyramid
      Right pyramidal frustum
     Regular Polyhedrons
      Tetrahedron
      Octahedron
Pyramid
A solid whose base is a polygon and whose lateral faces are triangles with a common vertex (apex) is called a pyramid. 
A right pyramid is a pyramid in which the line joining the centroid of the base (the point of coincidence of the medians) and the apex is perpendicular to the base.
A regular pyramid is a right pyramid whose base is a regular polygon and lateral faces are congruent isosceles triangles.
The volume of a pyramid is one third of the product of the area of the base and the perpendicular distance from the vertex to the base.
The surface area of a pyramid: S = B + Slat
The volume of a pyramid: V = 1/3 B h,
where B is the base area,  Slat  is the lateral surface area and h is the height of the pyramid.
Regular square pyramid
A regular square pyramid has square base and lateral faces are four congruent isosceles triangles making the same angle with the base.
   - surface
 - volume
Regular triangular pyramid
A regular triangular pyramid has an equilateral triangle base, and three congruent isosceles triangles as lateral faces making the same angle with the base.
R -the radius of the circumcircle,  r -the radius of the incircle 
   - surface
 - volume
Regular hexagonal pyramid
A regular hexagonal pyramid has a regular hexagon base, and six congruent isosceles triangles as lateral faces making the same angle with the base.
   - surface
 - volume
Right pyramidal frustum
B : B1 = (h + x)2 : x2
   - surface
P, P1 - bottom and top base perimeter  
- volume
     Regular Polyhedrons
      Tetrahedron
      Octahedron
Tetrahedron
 
   
Octahedron
 
   
   
The equilateral triangles are faces of, the tetrahedron (4-faced), the octahedron (8) and the icosahedron (20), while the dodecahedron consists of 12 regular pentagons.
Geometry and use of trigonometry contents - B
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