Paraleelogram

Tekst üüb Öömrang

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

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 Commonskategorii: Paraleelogram – Saamlang faan bilen of filmer