Prisma (Geometrii)

Tekst üüb Öömrang

En Prisma as en geomeetrisk grünjfiguur, huar det grünjflaak an det hoodflaak likedenang san an paraleel auerenööder lei. Sodenang as en Prisma bal detsalew üs en Türn, hää oober ei ünbedingt en Kreis üs grünjflaak. En likmiatag prisma hää en likmiatag grünjflaak, so üs t.b. det sääkshuket prisma uun det tiaknang rochts. Di lik wai tesken grünjflaak an hoodflaak as det hööchde $h$ faan't prisma.

En lik (A) an en sküüns (B) Prisma

Wan a mantel luadrocht üüb't grünjflaak stäänt, do as det en lik prisma, ööders as't en sküüns prisma. A mantel faan en lik prisma as faan rochthuken tuupsaat, bi't sküüns prisma san't paraleelogramen.

Bereegnangen

Bereegnangen bi en likmiatag prisma mä n huken, sidjenlengde a an hööchde h
	Algemian Prisma n	Kwadrootisk Prisma n = 4	Likmiatag Triihuksprisma n = 3
Grünjflaak $A_{g}$	$\left({\frac {n}{4}}\cot \!{\frac {\pi }{n}}\right)a^{2}$	$a^{2}$	${\frac {\sqrt {3}}{4}}\ a^{2}$
Rüm $V$	$\left({\frac {n}{4}}\cot \!{\frac {\pi }{n}}\right)a^{2}h$	$a^{2}h$	${\frac {\sqrt {3}}{4}}\ a^{2}h$
Areaal faan 2 x Grünjflaak + Mantel $O$	${\frac {an}{2}}\ \left(2h+a\ \cot {\frac {\pi }{n}}\right)$	$a^{2}+a{\sqrt {4h^{2}+a^{2}}}$	${\frac {3a}{4}}\left({\sqrt {3}}\ {\frac {a}{3}}+{\sqrt {4h^{2}+{\frac {a^{2}}{3}}}}\right)$
Amkuugelraadius $r_{u}$	${\frac {1}{2}}{\sqrt {h^{2}+{\frac {a^{2}}{\sin ^{2}{\frac {\pi }{n}}}}}}$	${\frac {1}{2}}{\sqrt {h^{2}+2a^{2}}}$	${\frac {1}{2}}{\sqrt {h^{2}+{\frac {4a^{2}}{3}}}}$
Banenwinkel faan't likmiatag grünjflaak $\alpha$	${\frac {n-2}{n}}\cdot 180^{\circ }$	$90^{\circ }$	$60^{\circ }$
Winkel tesken grünjflaak an mantel $\beta _{1}$	$90^{\circ }$	$90^{\circ }$	$90^{\circ }$
Winkel tesken a rochthuken $\beta _{2}$	${\frac {n-2}{n}}\cdot 180^{\circ }$	$90^{\circ }$	$60^{\circ }$
Rümwinkel uun a huken $\Omega$	${\frac {n-2}{n}}\cdot \pi \ \mathrm {sr}$	${\frac {\pi }{2}}\ \mathrm {sr}$	${\frac {\pi }{3}}\ \mathrm {sr}$

Luke uk diar

 Commonskategorii: Prisma – Saamlang faan bilen of filmer