Paraleelogram

Paraleelogram mä
• huken A, B, C, D
• sidjen a = c, b = d
• winkler α = γ, β = δ
• hööchde h_a ≠ h_b
• diagonaalen e, f

En Paraleelogram as en sjauerhuk, diar en Rütj liket, man a sidjen san ei aaltumaal likelung. A sidjen, diar jinauer lei, san oober likelung.

Bereegnangen

Bereegnangsformeln
Areaal	$A=a\cdot h_a=b\cdot h_b=\left||\overrightarrow{AB}\times \overrightarrow{AD}|\right|$ $A=a\cdot b\cdot \sin (\alpha )=a\cdot b\cdot \sin (\beta )=\frac{e\cdot f\cdot \sin (\theta )}{2}$
Amfaadang	$U=2\cdot a+2\cdot b=2\cdot (a+b)$
Banenwinkler	$\alpha =\gamma ,\beta =\delta ,\alpha +\beta =180^{\circ }$
Hööchde	$h_a=b\cdot \sin (\alpha )$
	$h_b=a\cdot \sin (\beta )$
Lengde faan a Diagonaalen (efter Kosinussats)	$\begin{array}{cc}e& =\sqrt{a^2+b^2-2\cdot a\cdot b\cdot \cos (\beta )}\\ & =\sqrt{a^2+b^2+2\cdot a\cdot b\cdot \cos (\alpha )}\end{array}$
	$\begin{array}{cc}f& =\sqrt{a^2+b^2-2\cdot a\cdot b\cdot \cos (\alpha )}\\ & =\sqrt{a^2+b^2+2\cdot a\cdot b\cdot \cos (\beta )}\end{array}$
Paraleelogramliknang	$e^2+f^2=2\cdot (a^2+b^2)$