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| Solid
Geometry, Pyramids
and Regular Polyhedrons |
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Pyramids |
Regular
square pyramid
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Regular triangular pyramid
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Regular hexagonal pyramid
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Right
pyramidal frustum |
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| 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. |
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| The surface
area of a pyramid: |
S
= B
+ Slat |
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| The volume of a pyramid: |
V
= 1/3 ·
B ·
h,
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| where
B is
the base area, Slat
is the lateral surface area and h
is the height of the
pyramid. |
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| Regular
square pyramid
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| A
regular square pyramid has square base and lateral faces are
four congruent isosceles triangles making the same angle with
the base. |
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| Regular triangular pyramid
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| A
regular triangular pyramid has an equilateral triangle base, and
three congruent isosceles triangles as lateral faces making the same angle with
the base. |
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| R
-the
radius of the circumcircle, r
-the radius of the incircle |
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-
surface |
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-
volume |
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| Regular hexagonal pyramid
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| A
regular hexagonal pyramid has a regular hexagon base, and six congruent isosceles triangles as lateral faces making the same angle with
the base. |
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| Right
pyramidal frustum |
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| B
: B1 = (h + x)2
: x2 |
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-
surface |
| P,
P1 - bottom
and top base perimeter |
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-
volume |
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Regular Polyhedrons |
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Tetrahedron |
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Octahedron |
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| Tetrahedron |
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| Octahedron |
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| 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. |
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| Beginning
Algebra Contents E |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
