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Solid
Geometry |
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Prisms |
Cube
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Rectangular prism
or rectangular parallelepiped
(cuboid)
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Right triangular prism
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Regular right triangular prism
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Regular right hexagonal prism
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Prism |
A
prism is a polyhedron (having five or more faces) with two parallel and congruent polygonal bases, so
that all cross-sections 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. |
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S
= 2B + Slat |
-
surface of a prism |
Slat = P ·
h |
-
lateral surface |
V
= B · h |
- volume
of a prism |
B
-area of
base, P
- perimeter of base, h
-height
of a prism |
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Cube
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A
solid with six identical square faces that are mutually
perpendicular. |
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- diagonal |
S
= 2B + Slat
= 2a2
+
4a2
= 6a2 |
-
surface |
V
= B · h = a2
· a = a3 |
- volume |
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Rectangular prism or
rectangular parallelepiped (cuboid)
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A
solid of which the six faces are mutually perpendicular
rectangles is called a rectangular parallelepiped or
a rectangular prism.
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- diagonal |
S
= 2B + Slat
= 2(ab + ac + bc) |
-
surface |
V
= B · h = a
· b · c |
-
volume |
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Right triangular prism
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A
right triangular prism is made of two triangular bases and three
rectangular faces with lateral edges perpendicular to the bases. |
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S
= 2B + Slat
= a
ha + (a + b
+ c)· h |
-
surface |
V
= B · h = 1/2 ·
a
ha · h |
-
volume |
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Regular right triangular prism
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A
prism made of two equilateral triangular bases and three
identical rectangular sides is called a regular right triangular
prism. |
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Regular right hexagonal prism
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A prism made of two regular hexagonal bases and six identical rectangular sides is called a regular right hexagonal prism. |
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