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1
'"`UNIQ--postMath-00000001-QINU`"'
2
'"`UNIQ--postMath-00000002-QINU`"'
3
'"`UNIQ--postMath-00000003-QINU`"'
4
'"`UNIQ--postMath-00000004-QINU`"'
5
'"`UNIQ--postMath-00000005-QINU`"'
6
'"`UNIQ--postMath-00000006-QINU`"'
7
'"`UNIQ--postMath-00000007-QINU`"'
8
'"`UNIQ--postMath-00000008-QINU`"'
9
'"`UNIQ--postMath-00000009-QINU`"'
10
'"`UNIQ--postMath-0000000A-QINU`"'
11
'"`UNIQ--postMath-0000000B-QINU`"'
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'"`UNIQ--postMath-0000000C-QINU`"'
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'"`UNIQ--postMath-0000000D-QINU`"'
14
'"`UNIQ--postMath-0000000E-QINU`"'
15
'"`UNIQ--postMath-0000000F-QINU`"'
16
'"`UNIQ--postMath-00000010-QINU`"'
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From Wikipedia, the free encyclopedia
This is an
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of this page, as edited by
Tet-Math2
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at
11:20, 17 June 2024
. The present address (URL) is a
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to this revision, which may differ significantly from the
current revision
.
Revision as of 11:20, 17 June 2024 by
Tet-Math2
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(
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O
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{\displaystyle Only\ \ In\ \ TriRectangular\ \ Tetrahedrons}
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{\displaystyle K={\Biggl [}{\frac {a^{2}+b^{2}+c^{2}}{2}}{\Biggr ]}={\Bigl [}x^{2}+y^{2}+z^{2}{\Bigr ]}={\Bigl [}a^{2}+z^{2}{\Bigr ]}={\Bigl [}b^{2}+y^{2}{\Bigr ]}={\Bigl [}c^{2}+z^{2}{\Bigr ]}}
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{\displaystyle K\ {\Bigl [}Constant{\Bigr ]}\ \ \ \ \ \ \ \ \ Given{\Bigl [}a,b,c{\Bigr ]}\ \ \ \ \ \ \ \ \ Given{\Bigl [}x,y,z{\Bigr ]}}
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{\displaystyle K={\Bigl [}a^{2}+z^{2}{\Bigr ]}\ \ \ \ \ \ \ \ \ a={\sqrt {_{\ }K-z^{2}\ \ }}\ \ \ \ \ \ z={\sqrt {_{\ }K-a^{2}\ \ }}}
K
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[
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b
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y
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{\displaystyle K={\Bigl [}b^{2}+y^{2}{\Bigr ]}\ \ \ \ \ \ \ \ \ b={\sqrt {_{\ }K-y^{2}\ \ }}\ \ \ \ \ \ y={\sqrt {_{\ }K-b^{2}\ \ }}}
K
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[
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x
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c
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{\displaystyle K={\Bigl [}c^{2}+x^{2}{\Bigr ]}\ \ \ \ \ \ \ \ \ c={\sqrt {_{\ }K-x^{2}\ \ }}\ \ \ \ \ \ x={\sqrt {_{\ }K-c^{2}\ \ }}}
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{\displaystyle V_{box}=xyz\ \ \ \ \ \ \ \ \ V_{tet}={\frac {\ xyz\ }{6}}}
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{\displaystyle A_{abc}={\frac {\ \ {\sqrt {x^{2}y^{2}+z^{2}{\Bigl [}x^{2}+y^{2}{\Bigr ]}\ }}\ \ \ }{2}}\ \ \ \ \ \ Area\ \ of\ \ Base}
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{\displaystyle h_{tet}\ ={\frac {xyz}{\ \ {\sqrt {\ x^{2}y^{2}+z^{2}{\Bigl [}x^{2}+y^{2}{\Bigr ]}\ }}\ \ }}\ \ \ \ \ Height\ \ of\ \ Tetrahedron}
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{\displaystyle A_{abc}={\frac {xyz}{\ 2h_{tet}}}\ \ \ \ A_{xy}={\frac {\ xy\ }{2}}\ \ \ \ A_{xz}={\frac {\ xz\ }{2}}\ \ \ \ A_{yz}={\frac {\ yz\ }{2}}\ \ \ \ Individual\ \ Areas\ \ of\ \ All\ \ Surfaces}
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{\displaystyle A_{tet}=A_{abc}+A_{xy}+A_{xz}+A_{yz}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Total\ \ Area\ \ of\ \ Tetrahedron}
A
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{\displaystyle A_{tet}={\frac {\ xy+z{\Bigl [}x+y{\Bigr ]}+{\sqrt {x^{2}y^{2}+z^{2}{\Bigl [}x^{2}+y^{2}{\Bigr ]}\ }}\ \ }{2}}\ \ \ \ \ Total\ \ Area\ \ of\ \ Tetrahedron}
a
=
14.4
b
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10
c
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12
{\displaystyle a=14.4\ \ \ \ \ b=10\ \ \ \ \ c=12}
x
=
9.037698822156002781875821128798
{\displaystyle x=9.037698822156002781875821128798}
y
=
11.210709165793214885544254958172
{\displaystyle y=11.210709165793214885544254958172}
z
=
4.2801869118065393196504607419769
{\displaystyle z=4.2801869118065393196504607419769}
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![{\displaystyle K={\Biggl [}{\frac {a^{2}+b^{2}+c^{2}}{2}}{\Biggr ]}={\Bigl [}x^{2}+y^{2}+z^{2}{\Bigr ]}={\Bigl [}a^{2}+z^{2}{\Bigr ]}={\Bigl [}b^{2}+y^{2}{\Bigr ]}={\Bigl [}c^{2}+z^{2}{\Bigr ]}}](/media/api/rest_v1/media/math/render/svg/22c121328727aa84d9a48db4bbfcfc58227f54fa)
![{\displaystyle K\ {\Bigl [}Constant{\Bigr ]}\ \ \ \ \ \ \ \ \ Given{\Bigl [}a,b,c{\Bigr ]}\ \ \ \ \ \ \ \ \ Given{\Bigl [}x,y,z{\Bigr ]}}](/media/api/rest_v1/media/math/render/svg/b0c562a6bc3d1acdff522da28f14c3f16259b264)
![{\displaystyle K={\Bigl [}a^{2}+z^{2}{\Bigr ]}\ \ \ \ \ \ \ \ \ a={\sqrt {_{\ }K-z^{2}\ \ }}\ \ \ \ \ \ z={\sqrt {_{\ }K-a^{2}\ \ }}}](/media/api/rest_v1/media/math/render/svg/b5a4faf53f131374160dbf121cc032d8083998a1)
![{\displaystyle K={\Bigl [}b^{2}+y^{2}{\Bigr ]}\ \ \ \ \ \ \ \ \ b={\sqrt {_{\ }K-y^{2}\ \ }}\ \ \ \ \ \ y={\sqrt {_{\ }K-b^{2}\ \ }}}](/media/api/rest_v1/media/math/render/svg/d72dacbb48f647ded53be02e63208d5911b89be7)
![{\displaystyle K={\Bigl [}c^{2}+x^{2}{\Bigr ]}\ \ \ \ \ \ \ \ \ c={\sqrt {_{\ }K-x^{2}\ \ }}\ \ \ \ \ \ x={\sqrt {_{\ }K-c^{2}\ \ }}}](/media/api/rest_v1/media/math/render/svg/6a7a1462479b5a1b55c0da817e535fedf3fd0d98)
![{\displaystyle A_{abc}={\frac {\ \ {\sqrt {x^{2}y^{2}+z^{2}{\Bigl [}x^{2}+y^{2}{\Bigr ]}\ }}\ \ \ }{2}}\ \ \ \ \ \ Area\ \ of\ \ Base}](/media/api/rest_v1/media/math/render/svg/bf63ec88aba6fc09360c7e1f6ff8a22abb912807)
![{\displaystyle h_{tet}\ ={\frac {xyz}{\ \ {\sqrt {\ x^{2}y^{2}+z^{2}{\Bigl [}x^{2}+y^{2}{\Bigr ]}\ }}\ \ }}\ \ \ \ \ Height\ \ of\ \ Tetrahedron}](/media/api/rest_v1/media/math/render/svg/cf922d8fc8e57b1ca59a7b9394a2caf3518833b3)
![{\displaystyle A_{tet}={\frac {\ xy+z{\Bigl [}x+y{\Bigr ]}+{\sqrt {x^{2}y^{2}+z^{2}{\Bigl [}x^{2}+y^{2}{\Bigr ]}\ }}\ \ }{2}}\ \ \ \ \ Total\ \ Area\ \ of\ \ Tetrahedron}](/media/api/rest_v1/media/math/render/svg/75757fc60e0ad467f11fa002ebe935cc92d45395)
