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# Mathematrix: MA TER/ Formelsammlung Geometrie

Geometrie der Ebene
Name Figur (Form) Umfang Fläche Andere Formeln
Allgemeines Dreieck ${\displaystyle u=a+b+c}$ ${\displaystyle A={\frac {a\cdot h_{a}}{2}}={\frac {b\cdot h_{b}}{2}}={\frac {c\cdot h_{c}}{2}}}$
Rechtwinkeliges Dreieck ${\displaystyle u=a+b+c}$ ${\displaystyle A={\frac {a\cdot b}{2}}}$ ${\displaystyle c^{2}={a^{2}+b^{2}}}$
${\displaystyle c={\sqrt {a^{2}+b^{2}}}}$
Gleichseitiges Dreieck ${\displaystyle u=3a}$ ${\displaystyle A={\frac {\sqrt {3}}{4}}\cdot a^{2}}$ ${\displaystyle h={\frac {\sqrt {3}}{2}}a}$
Rechteck ${\displaystyle u=2a+2b}$
${\displaystyle u=2(a+b)}$
${\displaystyle A={a\cdot b}}$ ${\displaystyle d^{2}={a^{2}+b^{2}}}$
${\displaystyle d={\sqrt {a^{2}+b^{2}}}}$
Quadrat ${\displaystyle u=4a}$ ${\displaystyle A={a^{2}}}$ ${\displaystyle d={\sqrt {2}}a}$
Raute (Rhombus) ${\displaystyle u=4a}$ ${\displaystyle A={\frac {e\cdot f}{2}}}$ ${\displaystyle \textstyle {a^{2}=({\frac {e}{2}})^{2}+({\frac {f}{2}})^{2}}}$
Parallelogramm ${\displaystyle u=2a+2b}$
${\displaystyle u=u=2(a+b)}$
${\displaystyle A={a\cdot h_{a}}={b\cdot h_{b}}}$
Trapez ${\displaystyle u=a+b+c+d}$ ${\displaystyle A={\frac {a+c}{2}}\cdot h}$
Kreis ${\displaystyle u=2\pi \ r}$
${\displaystyle u=\pi \ d}$
${\displaystyle A={\pi \ r^{2}}}$
${\displaystyle A={\frac {\pi \ d^{2}}{4}}}$
Kreisring ${\displaystyle u=2\pi \ (R+r)}$ ${\displaystyle A={\pi \ (R^{2}-r^{2})}}$

Geometrie des Raums
Name Figur (Form) Oberfläche Volumen Netz (falls möglich)
Würfel ${\displaystyle A_{O}=6a^{2}}$ ${\displaystyle V=a^{3}}$
Quader ${\displaystyle A_{O}=2ab+2ac+2bc}$ ${\displaystyle V=abc}$
Pyramide
{\displaystyle {\begin{aligned}A_{O}&=A_{G}&&+A_{M}\\&=a^{2}&&+2a\ h_{1}\end{aligned}}}

${\displaystyle \left[A_{O}=a(a+h_{1})\right]}$

wobei ${\displaystyle h_{1}={\sqrt {\left({\frac {a}{2}}\right)^{2}+h^{2}}}}$
${\displaystyle h_{1}\ }$ mit ${\displaystyle a_{1}\ }$ im Bild
${\displaystyle V={\frac {a^{2}\ h}{3}}}$
Tetraeder ${\displaystyle A_{O}={\sqrt {3}}a^{2}}$ ${\displaystyle V={\frac {{\sqrt {2}}a^{3}}{12}}}$
Zylinder {\displaystyle {\begin{aligned}A_{O}&=2\ \ A_{G}&&+A_{M}\\&=2\ \ \pi r^{2}&&+2\pi r\ h\end{aligned}}}

${\displaystyle \left[A_{O}=2\pi r(r+h)\right]}$
${\displaystyle V=\pi r^{2}\ h}$
Kegel {\displaystyle {\begin{aligned}A_{O}&=A_{G}&&+A_{M}\\&=\pi r^{2}&&+\pi r\ s\end{aligned}}}

${\displaystyle \left[A_{O}=\pi r(r+s)\right]}$

wobei ${\displaystyle s={\sqrt {r^{2}+h^{2}}}}$
${\displaystyle V={\frac {\pi r^{2}\ h}{3}}}$
Prisma[1] {\displaystyle {\begin{aligned}A_{O}&=2\ \ A_{G}&&+A_{M}\\&=\ \ {3{\sqrt {3}}}{}a^{2}&&+6a\ h\end{aligned}}}    ${\displaystyle V=\overbrace {{\frac {3{\sqrt {3}}}{2}}a^{2}} ^{A_{G}}\ \ \cdot h}$
Kugel ${\displaystyle A_{O}=4\pi r^{2}}$ ${\displaystyle \textstyle V={\frac {4}{3}}\pi r^{3}}$
Torus ${\displaystyle A_{O}=4\pi ^{2}rR\ }$ ${\displaystyle V=2\pi ^{2}r^{2}R}$
1. mit regelmäßigem Sechseck als Basis