Inkreisradius
r
i
=
a
1
2
(
1
+
2
)
{\displaystyle r_{i}=a\ {\frac {1}{2}}(1+{\sqrt {2}})}
a
=
2
r
i
(
2
−
1
)
{\displaystyle a=2r_{i}\ ({\sqrt {2}}-1)}
Umkreisradius
r
u
=
a
1
2
4
+
2
2
{\displaystyle r_{u}=a\ {\frac {1}{2}}{\sqrt {4+2{\sqrt {2}}}}}
r
u
=
a
1
+
1
2
{\displaystyle r_{u}=a\ {\sqrt {1+{\frac {1}{\sqrt {2}}}}}}
a
=
r
u
2
−
2
{\displaystyle a=r_{u}\ {\sqrt {2-{\sqrt {2}}}}}
Große Diagonale
d
1
=
a
4
+
2
2
=
2
r
u
{\displaystyle d_{1}=a\ {\sqrt {4+2{\sqrt {2}}}}\ =\ 2r_{u}}
Mittlere Diagonale
d
2
=
a
(
1
+
2
)
=
2
r
i
{\displaystyle d_{2}=a\ (1+{\sqrt {2}})\ =\ 2r_{i}}
Kleine Diagonale
d
3
=
a
2
+
2
=
r
u
2
{\displaystyle d_{3}=a\ {\sqrt {2+{\sqrt {2}}}}\ =\ r_{u}\,{\sqrt {2}}}
Zentriwinkel Fehler beim Parsen (MathML mit SVG- oder PNG-Rückgriff (empfohlen für moderne Browser und Barrierefreiheitswerkzeuge): Ungültige Antwort („Math extension cannot connect to Restbase.“) von Server „https://en.wikipedia.org/api/rest_v1/“:): {\displaystyle \alpha = \frac{360^\circ}{8} = 45^\circ }
Innenwinkel |
δ
=
180
∘
−
α
=
135
∘
{\displaystyle \delta =180^{\circ }-\alpha =135^{\circ }}
cos
δ
=
−
1
2
{\displaystyle \cos \delta ={\frac {-1}{\sqrt {2}}}}
Flächeninhalt
A
=
a
2
(
2
+
2
2
)
{\displaystyle A=a^{2}\ (2+2{\sqrt {2}})}
A
=
r
u
2
2
2
{\displaystyle A=r_{u}^{2}\ 2{\sqrt {2}}}
