"Areaal (Miat)" uun ööder spriakwiisen
Füsikaalisk grate
Nööm
Areaal Flaak
Formeltiaken
A {\displaystyle A} (area)
Hinget tuup mä
Lengde
At areaal as en miat för det grate faan en geomeetrisk objekt. Arealen san tau-dimensionaal, diar hiar geomeetrisk grünjfurmen tu üs at kwadroot , at rochthuk , triihuk of a kreis . Man uk a bütjensidjen faan trii-dimensionaal objekten üs kuugel , silinder of sjauerkaant san areaalen.
Areaalen faan enkelt geomeetrisk objekten
Bewerke
Objekt
Betiaknangen
Areaal A {\displaystyle A}
Kwadroot
Sidjenlengde a {\displaystyle a}
A = a 2 {\displaystyle A=a^{2}}
Rochthuk
Sidjenlengden a , b {\displaystyle a,\,b}
A = a ⋅ b {\displaystyle A=a\cdot b}
Triihuk
Grünjsidj g {\displaystyle g} , Hööchde h {\displaystyle h} luadrocht tu g {\displaystyle g}
A = g ⋅ h 2 {\displaystyle A={\frac {g\cdot h}{2}}}
Trapeets
Parallel tuenööder sidjen a , c {\displaystyle a,\,c} , Hööchde h {\displaystyle h} luadrocht tu a {\displaystyle a} an c {\displaystyle c}
A = a + c 2 ⋅ h {\displaystyle A={\frac {a+c}{2}}\cdot h}
Rütj
Diagonaalen d 1 {\displaystyle d_{1}} an d 2 {\displaystyle d_{2}}
A = d 1 ⋅ d 2 2 {\displaystyle A={\frac {d_{1}\cdot d_{2}}{2}}}
Paraleelogram
Sidjenlengde a {\displaystyle a} , Hööchde h a {\displaystyle h_{a}} luadrocht tu a {\displaystyle a}
A = a ⋅ h a {\displaystyle A=a\cdot h_{a}}
Kreis
Raadius r {\displaystyle r}
A = π r 2 {\displaystyle A=\pi r^{2}}
Elips
Grat an letj hualewaaksen a {\displaystyle a} an b {\displaystyle b}
A = π a b {\displaystyle A=\pi ab}
Likmiatag Sääkshuk
Sidjenlengde a {\displaystyle a}
A = 3 3 2 a 2 {\displaystyle A={\frac {3{\sqrt {3}}}{2}}a^{2}}
Areaalen (bütjensidjen) faan trii-dimensionaal objekten
Bewerke
Sjauerflaak Lik kreiskeegel mä ufwolet mantel Objekt
Betiaknangen
Areaal A {\displaystyle A}
Dööbel
Sidjenlengde a {\displaystyle a}
A = 6 a 2 {\displaystyle A=6a^{2}}
Sjauerkaant
Sidjenlengden a , b , c {\displaystyle a,\,b,\,c}
A = 2 ( a b + a c + b c ) {\displaystyle A=2(ab+ac+bc)}
Sjauerflaak
Sidjenlengde a {\displaystyle a}
A = 3 a 2 {\displaystyle A={\sqrt {3}}\,a^{2}}
Kuugel
Raadius r {\displaystyle r}
A = 4 π r 2 {\displaystyle A=4\pi r^{2}}
Türn
Grünjraadius r {\displaystyle r} , Hööchde h {\displaystyle h}
A = 2 π r ( r + h ) {\displaystyle A=2\pi r(r+h)}
Keegel
Grünjraadius r {\displaystyle r} , Hööchde h {\displaystyle h}
A = π r ( r + r 2 + h 2 ) {\displaystyle A=\pi r(r+{\sqrt {r^{2}+h^{2}}})}
Ring
Bütjenraadius R {\displaystyle R} , Banenraadius r {\displaystyle r}
A = 4 π 2 ⋅ R ⋅ r {\displaystyle A=4\pi ^{2}\cdot R\cdot r}