
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
+ S_{lat} 

The volume of a pyramid: 
V
= 1/3 ·
B ·
h, 


where
B is
the base area, S_{lat }
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. 



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. 



Right
pyramidal frustum 

B
: B_{1} = (h + x)^{2}
: x^{2} 



surface 
P,
P_{1}_{
} bottom
and top base perimeter 



volume 



Regular Polyhedrons 
Tetrahedron 
Octahedron 

Tetrahedron 




Octahedron 





The equilateral triangles are faces of, the tetrahedron (4faced), 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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