Egallatera triangulo estas triangulo, kiu havas ĉiujn tri laterojn egale longajn.

Ecoj

Krom ecoj de triangulo komunaj por ĉiu triangulo la egallatera triangulo havas plie tiujn ĉi ecojn:

• Egallatera triangulo estas akse simetriaj kun tri aksoj de simetrio, kiuj kondukas ĉiam tra vertico kaj tra centro de la kontraŭa latero.
• Ĉiuj internaj anguloj estas kongruaj kaj ilia grandeco estas 60°.

Perimetro

Perimetron de egallatera triangulo o oni kalkulas laŭ formulo:

o = 3 . a , kie a estas latero de egallatera triangulo

Areo

• Se la triangulo estas egallatera, la areo estas egala al unu kvarono de la kvadrato de unu latero por la kvadrata radiko de 3:

${\displaystyle A={\frac {{\sqrt {3}}\cdot a^{2}}{4}}}$

kie a estas unu latero de la triangulo.

Bazaj rilatoj

${\displaystyle =\,}$	${\displaystyle a\,}$	${\displaystyle h\,}$	${\displaystyle S\,}$	${\displaystyle r\,}$	${\displaystyle R\,}$	${\displaystyle L_{r}\,}$	${\displaystyle L_{R}\,}$	${\displaystyle S_{r}\,}$	${\displaystyle S_{R}\,}$
${\displaystyle a\,}$	${\displaystyle a\,}$	${\displaystyle {\frac {2h{\sqrt {3}}}{3}}}$	${\displaystyle 2{\sqrt {\frac {S{\sqrt {3}}}{3}}}}$	${\displaystyle 2r{\sqrt {3}}}$	${\displaystyle R{\sqrt {3}}}$	${\displaystyle {\frac {L_{r}{\sqrt {3}}}{\pi }}}$	${\displaystyle {\frac {L_{R}{\sqrt {3}}}{2\pi }}}$	${\displaystyle 2{\sqrt {\frac {3S_{r}}{\pi }}}}$	${\displaystyle {\sqrt {\frac {3S_{R}}{\pi }}}}$
${\displaystyle h\,}$	${\displaystyle {\frac {a{\sqrt {3}}}{2}}}$	${\displaystyle h\,}$	${\displaystyle {\sqrt {S{\sqrt {3}}}}}$	${\displaystyle 3r\,}$	${\displaystyle {\frac {3}{2}}R}$	${\displaystyle {\frac {3L_{r}}{2\pi }}}$	${\displaystyle {\frac {3L_{R}}{4\pi }}}$	${\displaystyle 3{\sqrt {\frac {S_{r}}{\pi }}}}$	${\displaystyle {\frac {3}{2}}{\sqrt {\frac {S_{R}}{\pi }}}}$
${\displaystyle S\,}$	${\displaystyle {\frac {a^{2}{\sqrt {3}}}{4}}}$	${\displaystyle {\frac {h^{2}{\sqrt {3}}}{3}}}$	${\displaystyle S\,}$	${\displaystyle 3r^{2}{\sqrt {3}}}$	${\displaystyle {\frac {3R^{2}{\sqrt {3}}}{4}}}$	${\displaystyle {\frac {3{L_{r}}^{2}{\sqrt {3}}}{4\pi ^{2}}}}$	${\displaystyle {\frac {3{L_{R}}^{2}{\sqrt {3}}}{16\pi ^{2}}}}$	${\displaystyle {\frac {3S_{r}{\sqrt {3}}}{\pi }}}$	${\displaystyle {\frac {3S_{R}{\sqrt {3}}}{4\pi }}}$
${\displaystyle r\,}$	${\displaystyle {\frac {a{\sqrt {3}}}{6}}}$	${\displaystyle {\frac {1}{3}}h}$	${\displaystyle {\frac {\sqrt {S{\sqrt {3}}}}{3}}}$	${\displaystyle r\,}$	${\displaystyle {\frac {1}{2}}R}$	${\displaystyle {\frac {L_{r}}{2\pi }}}$	${\displaystyle {\frac {L_{R}}{4\pi }}}$	${\displaystyle {\sqrt {\frac {S_{r}}{\pi }}}}$	${\displaystyle {\sqrt {\frac {S_{R}}{4\pi }}}}$
${\displaystyle R\,}$	${\displaystyle {\frac {a{\sqrt {3}}}{3}}}$	${\displaystyle {\frac {2}{3}}h}$	${\displaystyle {\frac {2{\sqrt {S{\sqrt {3}}}}}{3}}}$	${\displaystyle 2r\,}$	${\displaystyle R\,}$	${\displaystyle {\frac {L_{r}}{\pi }}}$	${\displaystyle {\frac {L_{R}}{2\pi }}}$	${\displaystyle 2{\sqrt {\frac {S_{r}}{\pi }}}}$	${\displaystyle {\sqrt {\frac {S_{R}}{\pi }}}}$
${\displaystyle L_{r}\,}$	${\displaystyle {\frac {\pi a{\sqrt {3}}}{3}}}$	${\displaystyle {\frac {2\pi h}{3}}}$	${\displaystyle {\frac {2\pi {\sqrt {S{\sqrt {3}}}}}{3}}}$	${\displaystyle 2\pi r}$	${\displaystyle \pi R}$	${\displaystyle L_{r}\,}$	${\displaystyle {\frac {L_{R}}{2}}}$	${\displaystyle 2{\sqrt {\pi S_{r}}}}$	${\displaystyle {\sqrt {\pi S_{R}}}}$
${\displaystyle L_{R}\,}$	${\displaystyle {\frac {2\pi a{\sqrt {3}}}{3}}}$	${\displaystyle {\frac {4\pi h}{3}}}$	${\displaystyle {\frac {4\pi {\sqrt {S{\sqrt {3}}}}}{3}}}$	${\displaystyle 4\pi r}$	${\displaystyle 2\pi R}$	${\displaystyle 2L_{r}}$	${\displaystyle L_{R}\,}$	${\displaystyle 4{\sqrt {\pi S_{r}}}}$	${\displaystyle 2{\sqrt {\pi S_{R}}}}$
${\displaystyle S_{r}\,}$	${\displaystyle {\frac {\pi a^{2}}{12}}}$	${\displaystyle {\frac {\pi h^{2}}{9}}}$	${\displaystyle {\frac {\pi S{\sqrt {3}}}{9}}}$	${\displaystyle \pi r^{2}}$	${\displaystyle {\frac {\pi R^{2}}{4}}}$	${\displaystyle {\frac {{L_{r}}^{2}}{4\pi }}}$	${\displaystyle {\frac {{L_{R}}^{2}}{16\pi }}}$	${\displaystyle S_{r}\,}$	${\displaystyle {\frac {S_{R}}{4}}}$
${\displaystyle S_{R}\,}$	${\displaystyle {\frac {\pi a^{2}}{3}}}$	${\displaystyle {\frac {4\pi h^{2}}{9}}}$	${\displaystyle {\frac {4\pi S{\sqrt {3}}}{9}}}$	${\displaystyle 4\pi r^{2}}$	${\displaystyle \pi R^{2}}$	${\displaystyle {\frac {{L_{r}}^{2}}{\pi }}}$	${\displaystyle {\frac {{L_{R}}^{2}}{4\pi }}}$	${\displaystyle 4S_{r}}$	${\displaystyle S_{R}\,}$

Vidu ankaŭ

• Pluredro
• Triangulo
• Simetria triangulo