
Solid
Geometry 


Prisms 
Cube

Rectangular prism
or rectangular parallelepiped
(cuboid)

Right triangular prism

Regular right triangular prism

Regular right hexagonal prism







Prism 
A
prism is a polyhedron (having five or more faces) with two parallel and congruent polygonal bases, so
that all crosssections taken parallel to the bases are also congruent with the
bases, thus all lateral faces (sides) are parallelograms. 
Lateral
faces meet in line segments called lateral
edges. 
A
right prism is one whose lateral
faces and lateral edges are perpendicular to its bases. The
lateral faces of a right prism are all rectangles, and the
height of a right prism is equal to the length of its lateral
edge. 
A
regular prism has regular polygons as bases. A regular
polygon is one that has all sides equal in length and all angles
equal in measure. 
Thus,
a right regular prism is one with
regular polygon bases and perpendicular rectangular lateral
sides. 


S
= 2B + S_{lat} 

surface of a prism 
S_{lat} = P ·
h 

lateral surface 
V
= B · h 
 volume
of a prism 
B
area of
base, P
 perimeter of base, h
height
of a prism 



Cube

A
solid with six identical square faces that are mutually
perpendicular. 





 diagonal 
S
= 2B + S_{lat}
= 2a^{2
} +
4a^{2}
= 6a^{2} 

surface 
V
= B · h = a^{2
}· a = a^{3 } 
 volume 



Rectangular prism or
rectangular parallelepiped (cuboid)

A
solid of which the six faces are mutually perpendicular
rectangles is called a rectangular parallelepiped or
a rectangular prism.




 diagonal 
S
= 2B + S_{lat}
= 2(ab + ac + bc) 

surface 
V
= B · h = a^{
}· b · c 

volume 



Right triangular prism

A
right triangular prism is made of two triangular bases and three
rectangular faces with lateral edges perpendicular to the bases. 


S
= 2B + S_{lat}
= a^{
}h_{a } + (a + b
+ c)· h 

surface 
V
= B · h = 1/2 ·
a^{
}h_{a} · h 

volume 



Regular right triangular prism

A
prism made of two equilateral triangular bases and three
identical rectangular sides is called a regular right triangular
prism. 



Regular right hexagonal prism

A prism made of two regular hexagonal bases and six identical rectangular sides is called a regular right hexagonal prism. 










Geometry
and use of trigonometry contents  B 



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